%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
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% pdfの栞の字化けを防ぐ
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% テーマ
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% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
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%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
%\usetikzlibrary{calc}
%\usetikzlibrary{arrows.meta,patterns,angles,intersections,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
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\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\newcommand{\maruwaku}[1]{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
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\newcommand{\hooklen}[2]{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan!50}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

%\setbeamercolor{frametitle}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{palette primary}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{frametitle}{bg=CUDOrange}
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\begin{document}

\title{プレ高数学科}\author{gbb60166}

\def\noteq{%
\,\rlap{$=$}\setbox0\hbox{$=$}\makebox[\the\wd0]{\hss\(\backslash\)\hss}\,
}

%　斜線（１文字を消す）x
\def\sshasen{\kern-0.5em\tikz[baseline=2pt]
	\draw[line width=2pt, CUDRed](0,0.6)--(0.4,0);}

%■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■

\begin{frame}[t]
\frametitle{指数を使った書き方、対数を使った書き方}
\begin{minipage}[t]{0.36\textwidth}
\begin{beamercolorbox}[wd=\textwidth, ht=4ex,sep=2pt,shadow=true,
	rounded=true, center]{CUDCream}
\Large
\( \text{\fontsize{34}{34}\selectfont\textcolor{CUDGreen}{★}}^{\text{\fontsize{18}{18}\selectfont\textcolor{CUDRed}{●}}}
=\text{\textcolor{CUDBlue}{▲}} \)
\end{beamercolorbox}
\end{minipage}
\quad と\quad
\begin{minipage}[t]{0.45\textwidth}
\begin{beamercolorbox}[wd=\textwidth,ht=4ex, sep=2pt,shadow=true,
	rounded=true, center]{CUDBrightCyan}
\Large
\( \log_{\text{\fontsize{18}{18}\selectfont\textcolor{CUDGreen}{★}}} \text{\textcolor{CUDBlue}{▲}}=\text{\textcolor{CUDRed}{●}} \)
\end{beamercolorbox}
\end{minipage}

\vskip3ex
\centerline{は、同じです。（書き方が違うけど…）}
%（ただし★は$1$でない正の数、△は正の数）
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{覚え方}
\begin{minipage}[t]{0.36\textwidth}
\begin{beamercolorbox}[wd=\textwidth, ht=4ex,sep=2pt,shadow=true,
	rounded=true, center]{CUDCream}
\Large
\( \text{\textcolor{CUDGreen}{\ajMaru{1}}}^{\text{\fontsize{18}{18}\selectfont\textcolor{CUDRed}{\ajMaru{2}}}}
=\text{\textcolor{CUDBlue}{\ajMaru{3}}} \)
\end{beamercolorbox}
\end{minipage}
\quad と\quad
\begin{minipage}[t]{0.45\textwidth}
\begin{beamercolorbox}[wd=\textwidth,ht=4ex, sep=2pt,shadow=true,
	rounded=true, center]{CUDBrightCyan}
\Large
\( \log_{\text{\fontsize{18}{18}\selectfont\textcolor{CUDGreen}{\ajMaru{1}}}} \text{\textcolor{CUDBlue}{\ajMaru{3}}}=\text{\textcolor{CUDRed}{\ajMaru{2}}} \)
\end{beamercolorbox}
\end{minipage}

\vskip3ex
\centerline{私はこう覚えています。}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log \)の表し方（その$1$）}
\huge
\vspace*{-1ex}
\centerline{\alt<2->{\( \textcolor{CUDGreen}{3}^
	{\textcolor{CUDRed}{2}}=\textcolor{CUDBlue}{9} \)}
	{\( 3^2=9 \)}}\pause
\vskip-0.6ex
\centerline{\Large\ajDownWArrow}

\centerline{\( \alt<3->{\log_{\makebox[1ex]{$\scriptstyle3$}} \makebox[0.8em]{$9$}=\makebox[0.8em]{$2$}}{\log_{\makebox[1ex]{\fontsize{18}{18}\selectfont\textcolor{CUDGreen}{\ajMaru{1}}}} \makebox[0.8em]{\textcolor{CUDBlue}{\ajMaru{3}}}=\makebox[0.8em]{\textcolor{CUDRed}{\ajMaru{2}}}} \)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log \)の表し方（その$2$）}
\huge
\vspace*{-1ex}
\centerline{\( 5^3=125 \)}\pause

%\centerline{\textcolor{CUDRed}{\Large\ajDownBArrow}}
\vskip-0.6ex
\centerline{\Large\ajDownWArrow}

\centerline{\( \log_5 125=3 \)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log \)の表し方（その$3$）}
\huge
\vspace*{-1ex}
\centerline{\( 2^{-4}=\tfrac{1}{\,16\,} \)}\pause

%\centerline{\textcolor{CUDRed}{\Large\ajDownBArrow}}
\vskip-0.6ex
\centerline{\Large\ajDownWArrow}

\centerline{\( \log_2 \tfrac{1}{\,16\,}=-4 \)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log \)の表し方（その$4$）}
\huge
\vspace*{-1ex}
\centerline{\( \log_4 64=3 \)}\pause

%\centerline{\textcolor{CUDRed}{\Large\ajDownBArrow}}
\centerline{\Large\ajDownWArrow}

\centerline{\( 4^3=64 \)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log \)の表し方（その$5$）}
\huge
\vspace*{-1ex}
\centerline{\( \log_7 49=2 \)}\pause

%\centerline{\textcolor{CUDRed}{\Large\ajDownBArrow}}
\centerline{\Large\ajDownWArrow}

\centerline{\( 7^2=49 \)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log \)の表し方（その$6$）}
\huge
\vspace*{-1ex}
\centerline{\( \log_6 \tfrac{1}{\,216\,}=-3 \)}\pause

\bigskip
\centerline{\Large\ajDownWArrow}

\centerline{\( 6^{-3}=\tfrac{1}{\,216\,} \)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}}
	\textcolor{CUDRed}{1}=0 \)\quad が成り立ちます}
\vskip-1ex
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{yellow50}{fg=black,bg=yellow!50}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{yellow50}
	\( \log_7 1=0 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 7^0=1 \)}
\end{beamercolorbox}
\end{minipage}
\hfill
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{blue20}{fg=black,bg=blue!20}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{blue20}
	\( \log_{10} 1=0 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 10^0=1 \)}
\end{beamercolorbox}
\end{minipage}

\bigskip
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{sbcpink}{fg=black,bg=pink!75}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{sbcpink}
	\( \log_{2.5} 1=0 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 2.5^0=1 \)}
\end{beamercolorbox}
\end{minipage}
\hfill
\visible<2->{\textcolor{CUDRed}{\footnotesize
	\shortstack{以\\[-2pt]前\\[-2pt]学\\[-2pt]習\\[-2pt]済\\[-2pt]み}}
	}
\hfill
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{sbcCUDBrightGreen}{fg=black,bg=CUDBrightGreen!75}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{sbcCUDBrightGreen}
	\( \log_{\tfrac{\,3\,}{4}} 1=0 \)
	
	\visible<2->{\ajDownWArrow
	
		\( \left(\tfrac{\,3\,}{4}\right)^0=1 \)}
\end{beamercolorbox}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize\textcolor{CUDGreen}{★}}}
	\text{\textcolor{CUDGreen}{★}}=1 \)\quad が成り立ちます}
\vskip-1ex
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{yellow50}{fg=black,bg=yellow!50}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{yellow50}
	\( \log_5 5=1 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 5^1=5 \)}
\end{beamercolorbox}
\end{minipage}
\hfill
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{blue20}{fg=black,bg=blue!20}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{blue20}
	\( \log_4 4=1 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 4^1=4 \)}
\end{beamercolorbox}
\end{minipage}

\bigskip
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{sbcpink}{fg=black,bg=pink!75}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{sbcpink}
	\( \log_{3.6} 3.6=1 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 3.6^1=3.6 \)}
\end{beamercolorbox}
\end{minipage}
\hfill
\visible<2->{\textcolor{CUDRed}{\small
	\shortstack{当\\[-2pt]然\\[-2pt]だ\\[-2pt]ね}}
	}
\hfill
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{sbcCUDBrightGreen}{fg=black,bg=CUDBrightGreen!75}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{sbcCUDBrightGreen}
	\( \log_{\tfrac{\,1\,}{3}} \tfrac{\,1\,}{3}=1 \)
	
	\visible<2->{\ajDownWArrow
	
		\( \left(\tfrac{\,1\,}{3}\right)^1=\tfrac{\,1\,}{3} \)}
\end{beamercolorbox}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize\textcolor{CUDGreen}{★}}}
	\text{\textcolor{CUDGreen}{★}}^
	{\text{\footnotesize\textcolor{CUDRed}{●}}}
	=\text{\textcolor{CUDRed}{●}} \)\quad が成り立ちます}
\vskip-1ex
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{yellow50}{fg=black,bg=yellow!50}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{yellow50}
	\( \log_3 3^5=5 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 3^5=3^5 \)}
\end{beamercolorbox}
\end{minipage}
\hfill
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{blue20}{fg=black,bg=blue!20}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{blue20}
	\( \log_{11} 11^2=2 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 11^2=11^2 \)}
\end{beamercolorbox}
\end{minipage}

\bigskip
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{sbcpink}{fg=black,bg=pink!75}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{sbcpink}
	\( \log_7 7^{-3}=-3 \)
	
	\visible<2->{\ajDownWArrow
	
		\( 7^{-3}=7^{-3} \)}
\end{beamercolorbox}
\end{minipage}
\hfill
\visible<2->{\textcolor{CUDRed}{\small
	\shortstack{当\\[-2pt]然\\[-2pt]だ\\[-2pt]！}}
	}
\hfill
\begin{minipage}[t]{0.4\textwidth}
\setbeamercolor{sbcCUDBrightGreen}{fg=black,bg=CUDBrightGreen!75}
\begin{beamercolorbox}[wd=\textwidth, sep=2pt,shadow=true,
	rounded=true, center]{sbcCUDBrightGreen}
	\( \log_{\tfrac{\,3\,}{4}} \left(\tfrac{\,3\,}{4}\right)^6=6 \)
	
	\visible<2->{\ajDownWArrow
	
		\( \left(\tfrac{\,3\,}{4}\right)^6
			=\left(\tfrac{\,3\,}{4}\right)^6 \)}
\end{beamercolorbox}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{習うより慣れろ！}
\(\log\)の書き方でピンとこないときは、指数の書き方に
してみると分かりやすいだろう。

\bigskip
\(\log\)の書き方のままでもスムーズに計算できるようになるには、
自分で問題をたくさん解くことが必要だ。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}} \text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{{}+{}}\log_{\text{\footnotesize ★}} \text{\textcolor{CUDGreen}{▲}}=%
\log_{\text{\footnotesize ★}} (\text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{\times}\text{\textcolor{CUDGreen}{▲}}) \)}
\vspace*{-3ex}
\large
\begin{eqnarray*}
\log_5 3 + \log_5 6 \pause &=& \log_5 (3\times6) \\[2ex] \pause
&=& \log_5 18 \quad\text{\□答}
\end{eqnarray*}

\pause
\centerline{\textcolor{CUDRed}{たし算はかけ算へ！}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}} \text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{{}+{}}\log_{\text{\footnotesize ★}} \text{\textcolor{CUDGreen}{▲}}=%
\log_{\text{\footnotesize ★}} (\text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{\times}\text{\textcolor{CUDGreen}{▲}}) \)}
\vspace*{-3ex}
\large
\begin{eqnarray*}
\log_2 7 + \log_2 4 \pause &=& \log_2 (7\times4) \\[2ex] \pause
&=& \log_2 28 \quad\text{\□答}
\end{eqnarray*}

\centerline{\textcolor{CUDRed}{たし算はかけ算へ！}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}} \text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{{}+{}}\log_{\text{\footnotesize ★}} \text{\textcolor{CUDGreen}{▲}}=%
\log_{\text{\footnotesize ★}} (\text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{\times}\text{\textcolor{CUDGreen}{▲}}) \)}
\large
\( \log_{\textcolor{CUDRed}{3}} 8 + \log_{\textcolor{CUDRed}{7}} 5 \)は計算できません。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}} \text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{{}-{}}\log_{\text{\footnotesize ★}} \text{\textcolor{CUDGreen}{▲}}=
\log_{\text{\footnotesize ★}} \tfrac{\,\text{\textcolor{CUDRed}{●}}\,}{\text{\textcolor{CUDGreen}{▲}}}
%分子の文字が切れるので見えない支柱を入れる
\rule[-16pt]{0pt}{44pt}
 \)}
\vspace*{-3ex}
\large
\begin{eqnarray*}
\log_3 48 - \log_3 8 \pause &=& \log_3 \tfrac{48}{8} \\[2ex] \pause
&=& \log_3 6 \quad\text{\□答}
\end{eqnarray*}

\pause
\centerline{\textcolor{CUDRed}{ひき算は分数（わり算）へ！}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}} \text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{{}-{}}\log_{\text{\footnotesize ★}} \text{\textcolor{CUDGreen}{▲}}=
\log_{\text{\footnotesize ★}} \tfrac{\,\text{\textcolor{CUDRed}{●}}\,}{\text{\textcolor{CUDGreen}{▲}}}
%分子の文字が切れるので見えない支柱を入れる
\rule[-16pt]{0pt}{44pt}
 \)}
\vspace*{-3ex}
\large
\begin{eqnarray*}
\log_7 12 - \log_7 4 \pause &=& \log_7 \tfrac{12}{4} \\[2ex] \pause
&=& \log_7 3 \quad\text{\□答}
\end{eqnarray*}

\centerline{\textcolor{CUDRed}{ひき算は分数（わり算）へ！}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize ★}} \text{\textcolor{CUDRed}{●}}\textcolor{CUDBlue}{{}-{}}\log_{\text{\footnotesize ★}} \text{\textcolor{CUDGreen}{▲}}=
\log_{\text{\footnotesize ★}} \tfrac{\,\text{\textcolor{CUDRed}{●}}\,}{\text{\textcolor{CUDGreen}{▲}}}
%分子の文字が切れるので見えない支柱を入れる
\rule[-16pt]{0pt}{44pt}
 \)}
\large
\( \log_{\textcolor{CUDRed}{7}} 18 - \log_{\textcolor{CUDRed}{2}} 9 \)は計算できません。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{対数の計算（応用編）}
\vspace*{-5ex}
\begin{eqnarray*}
& & \log_7 6 + \log_7 8 - \log_7 3 \\[1ex] \pause
&=& \hooklen{\log_7 6 + \log_7 8}{\log_7 (6\times8)} - \log_7 3 \\[1ex] \pause
&=& \hooklen{\log_7 6 + \log_7 8 - \log_7 3}{\log_7 \myfrac{\ 6\times8\ }{3}} \\[1ex] \pause
&=& \log_7 \myfrac{{}^{\textcolor{CUDRed}{\textstyle 2}}6\sshasen\times8 }{3\sshasen_{\textcolor{CUDRed}{\textstyle 1}}} \pause = \log_7 16 \quad\text{\□答}
\end{eqnarray*}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize\textcolor{CUDRed}{★}}} \text{\textcolor{CUDGreen}{▲}}^{\text{\footnotesize\textcolor{CUDBlue}{●}}}=\text{\textcolor{CUDBlue}{●}}\log_{\text{\footnotesize\textcolor{CUDRed}{★}}} \text{\textcolor{CUDGreen}{▲}} \)}
\vspace*{-3ex}
\begin{eqnarray*}
\log_5 8 \pause &=& \phantom{3}\log_5 2^3 \\[1ex] \pause
&=& 3 \log_5 2  \quad\text{\□答}\\ \pause
(&=& 3\!\times\! \log_5 2 \text{のことです})
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \log_{\text{\footnotesize\textcolor{CUDRed}{★}}} \text{\textcolor{CUDGreen}{▲}}^{\text{\footnotesize\textcolor{CUDBlue}{●}}}=\text{\textcolor{CUDBlue}{●}}\log_{\text{\footnotesize\textcolor{CUDRed}{★}}} \text{\textcolor{CUDGreen}{▲}} \)}
\vspace*{-3ex}
\begin{eqnarray*}
\log_7 81 \pause &=& \phantom{4}\log_7 3^4 \\[1ex] \pause
&=& 4 \log_7 3  \quad\text{\□答}\\ \pause
(&=& 4\!\times\! \log_7 3 \text{のことです})
\end{eqnarray*}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{対数の計算（応用編）}

\vspace*{-5ex}
\begin{eqnarray*}
& & \log_3 12+\log_3 6-3\log_3 2 \\[1ex] \pause
&=& \log_3 12+\log_3 6-\phantom{3}\log_3 2^3 \\[1ex] \pause
&=& \hooklen{\log_3 12+\log_3 6-3\log_3 2}{\log_3 \myfrac{12\times6}{2^3}} \\[1ex] \pause
&=& \log_3 9 \pause =\log_3 3^2 \pause = 2 \quad\text{\□答}
\end{eqnarray*}

\centerline{前、学習した\ 
\colorbox{CUDCream}{\( \ \log_{\text{\footnotesize\textcolor{CUDGreen}{★}}}
	\text{\textcolor{CUDGreen}{★}}^
	{\text{\footnotesize\textcolor{CUDRed}{●}}}
	=\text{\textcolor{CUDRed}{●}} \ \)}\ を使った}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{対数の計算（応用編）}

\vspace*{-5ex}
\begin{eqnarray*}
& & 2\log_6 \sqrt{3}+\log_6 12 \\[1ex] \pause
&=& \log_6 \sqrt{3}\,{}^2+\log_6 12 \\[1ex] \pause
&=& \log_6 \hooklen{\sqrt{3}\,{}^2}{3}+\log_6 12 \\[1ex] \pause
&=& \quad \log_6 (3\times12) \\[1ex] \pause
&=& \log_6 36 \pause = \log_6 6^2 \pause = 2 \quad\text{\□答}
\end{eqnarray*}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{底の変換 \quad \( \log_{\text{\footnotesize\textcolor{CUDRed}{★}}} \text{\textcolor{CUDGreen}{●}}=%
\myfrac{\ \log_{\text{\footnotesize\textcolor{CUDBlue}{▲}}} \text{\textcolor{CUDGreen}{●}}\ }{ \log_{\text{\footnotesize\textcolor{CUDBlue}{▲}}} \text{\textcolor{CUDRed}{★}}} \)}
ただし\(\text{\textcolor{CUDRed}{★}} \noteq 1, \quad%
\text{\textcolor{CUDBlue}{▲}} \noteq 1 \)の正の数字

\vspace*{-1ex}
\[ \log_2 5=\myfrac{\ \log_3 5 \ }{\log_3 2}\quad\text{\□答} \]

\[ \log_3 7=\myfrac{\ \log_4 7 \ }{\log_4 3}\quad\text{\□答} \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{底の変換 \quad \( \log_{\text{\footnotesize\textcolor{CUDRed}{★}}} \text{\textcolor{CUDGreen}{●}}=%
\myfrac{\ \log_{\text{\footnotesize\textcolor{CUDBlue}{▲}}} \text{\textcolor{CUDGreen}{●}}\ }{\log_{\text{\footnotesize\textcolor{CUDBlue}{▲}}} \text{\textcolor{CUDRed}{★}}} \)}
\vspace*{-3ex}
\begin{eqnarray*}
\log_9 27 \pause &=& \myfrac{\ \log_3 27 \ }{\log_3 9} \pause =\myfrac{\ \log_3 3^3 \ }{\log_3 3^2} \pause =\myfrac{\,3\,}{2} \ \text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\end{document}

