Contoh Soal 1 Fungsi Logaritma

$\begin{array}{ll}\\ 1.&\textrm{Nilai dari}\: \: ^{2}\log \displaystyle \frac{1}{32}\: \: \textrm{adalah}\: ...\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle -7\\ \color{red}\textrm{b}.&\displaystyle -5\\ \textrm{c}.& \displaystyle -3\\ \textrm{d}.& \displaystyle -2\\ \textrm{e}.& 5 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}&=\: ^{2}\log \displaystyle \frac{1}{32}\\ &=\: ^{2^{1}}\log 2^{-5}\\ &=\displaystyle \frac{-5}{1}\times \: ^{2}\log 2\\ &=-5\\ &\\ & \end{aligned} \end{array}$

$\begin{array}{ll}\\ 2.&\textrm{Nilai dari}\: \: ^{0,333...}\log 0,111....\: \: \textrm{adalah}\: ...\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{3}\\ \textrm{b}.&\displaystyle \frac{1}{2}\\ \color{red}\textrm{c}.& 2\\ \textrm{d}.& 3\\ \textrm{e}.& 6 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}&=\: ^{0,333...}\log 0,111...\\ &=\: ^{\frac{1}{3}}\log \frac{1}{9}\\ &=\: ^{\frac{1}{3}}\log \left (\frac{1}{3} \right )^{2}\\ &=2 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 3.&\textrm{Nilai dari}\: \: ^{5}\log 25\sqrt{5}\: \: \textrm{adalah}\: ...\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&\displaystyle \frac{5}{2}\\ \textrm{b}.&\displaystyle \frac{3}{2}\\ \textrm{c}.& \displaystyle \frac{1}{2}\\ \textrm{d}.& \displaystyle 2\\ \textrm{e}.& 3 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}&=\: ^{5}\log 25\sqrt{5}\\ &=\: ^{5^{1}}\log 5^{2}.5^{\frac{1}{2}}\\ &=\: ^{5^{1}}\log 5^{\frac{5}{2}}\\ &=\displaystyle \frac{\frac{5}{2}}{1}\times \: ^{5}\log 5\\ &=\displaystyle \frac{5}{2} \end{aligned} \end{array}$

$\begin{array}{ll}\\ 4.&\textrm{Nilai dari}\: \: ^{\sqrt{3}}\log 81\: \: \textrm{adalah}\: ...\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 12\\ \textrm{b}.&\displaystyle 10\\ \textrm{c}.& \displaystyle 9\\ \color{red}\textrm{d}.& \displaystyle 8\\ \textrm{e}.& 6 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}&=\: ^{\sqrt{3}}\log 81\\ &=\: ^{\displaystyle 3^{\frac{1}{2}}}\log 3^{4}\\ &=\displaystyle \frac{4}{\frac{1}{2}}\times \: ^{3}\log 3\\ &=8 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 5.&\textrm{Nilai dari}\: \: ^{\frac{1}{3}}\log \displaystyle \frac{1}{243}\: \: \textrm{adalah}\: ...\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 6\\ \color{red}\textrm{b}.&\displaystyle 5\\ \textrm{c}.& \displaystyle 4\\ \textrm{d}.& \displaystyle 3\\ \textrm{e}.& \displaystyle 2 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}&=\: ^{\frac{1}{3}}\log \displaystyle \frac{1}{243}\\ &=\: ^{\left (\frac{1}{3} \right )^{1}}\log \displaystyle \left (\frac{1}{3} \right )^{5}\\ &=\displaystyle \frac{5}{1}\times \: ^{\frac{1}{3}}\log \frac{1}{3}\\ &=5 \end{aligned} \end{array}$