Contoh Soal 2 Fungsi Eksponen (Matematika Peminatan Kelas X)

$\begin{array}{ll}\\ 6.&\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi}\\ &\displaystyle 5^{2}\left ( \left ( \displaystyle \frac{1}{25} \right )^{2x+6} \right )^{\frac{1}{6}}=\displaystyle \frac{1}{25} \: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&-5\\ \textrm{b}.&-4\\ \textrm{c}.&-3\\ \textrm{d}.&1\\ \textrm{e}.&3 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}\displaystyle 5^{2}\left ( \left ( \displaystyle \frac{1}{25} \right )^{2x+6} \right )^{\frac{1}{6}}&=\displaystyle \frac{1}{25}\\ 25.\displaystyle 5^{2}\left ( \left ( \displaystyle \frac{1}{25} \right )^{2x+6} \right )^{\frac{1}{6}}&=1\\ 5^{2}.5^{2}.5^{-\frac{4x+12}{6}}&=5^{0}\\ 5^{2+2-\frac{2}{3}x-2}&=5^{0}\\ \displaystyle 2+2-\frac{2}{3}x-2&=0\\ 2-\displaystyle \frac{2}{3}x&=0\\ -\displaystyle \frac{2}{3}x&=-2\\ x&=3 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 7.&(\textbf{UM-UGM 03})\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi}\\ &\left ( \displaystyle \frac{1}{25} \right )^{x-\frac{5}{2}}=\sqrt{\displaystyle \frac{625}{5^{2-x}}} \: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{3}{5}\\ \color{red}\textrm{b}.&\displaystyle \frac{8}{5}\\ \textrm{c}.&2\\ \textrm{d}.&3\\ \textrm{e}.&5 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}\left ( \displaystyle \frac{1}{25} \right )^{x-\frac{5}{2}}&=\sqrt{\displaystyle \frac{625}{5^{2-x}}}\\ 5^{-2x+5}&=5^{\frac{1}{2}(4-(2-x))}\\ -2x+5&=\displaystyle \frac{1}{2}(4-2+x)\\ -4x+10&=2+x\\ -5x&=2-10\\ x&=\displaystyle \frac{-8}{-5}\\ &=\frac{8}{5} \end{aligned} \end{array}$

$\begin{array}{ll}\\ 8.&\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi}\\ &2^{\frac{x}{3}-1}=16 \: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&5\\ \textrm{b}.&10\\ \color{red}\textrm{c}.&15\\ \textrm{d}.&20\\ \textrm{e}.&25 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}2^{\frac{x}{3}-1}&=16\\ 2^{\frac{x}{3}-1}&=2^{4}\\ \displaystyle \frac{x}{3}-1&=4\\ \displaystyle \frac{x}{3}&=5\\ x&=15 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 9.&(\textbf{SPMB 05})\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi}\\ &\displaystyle \frac{\sqrt[3]{(0,08)^{7-2x}}}{(0,2)^{-4x+5}}=1 \: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&-3\\ \textrm{b}.&-2\\ \color{red}\textrm{c}.&-1\\ \textrm{d}.&0\\ \textrm{e}.&1 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}\displaystyle \frac{\sqrt[3]{(0,08)^{7-2x}}}{(0,2)^{-4x+5}}&=1\\ \sqrt[3]{(0,08)^{7-2x}}&=(0,2)^{-4x+5}\\ (0,2)^{\frac{3(7-2x)}{3}}&=(0,2)^{-4x+5}\\ \displaystyle 7-2x&=-4x+5\\ 4x-2x&=5-7\\ 2x&=-2\\ x&=-1 \end{aligned} \end{array}$

$\begin{array}{l}\\ 10.&(\textbf{SPMB 05})\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi}\\ &\displaystyle \frac{\sqrt[3]{\displaystyle \frac{1}{9^{2-x}}}}{27}=3^{x+1} \: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&-16\\ \textrm{b}.&-7\\ \textrm{c}.&4\\ \textrm{d}.&5\\ \textrm{e}.&6 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}\displaystyle \frac{\sqrt[3]{\displaystyle \frac{1}{9^{2-x}}}}{27}&=3^{x+1}\\ \sqrt[3]{\displaystyle \frac{1}{9^{2-x}}}&=27\times 3^{x+1}\\ \sqrt[3]{3^{-2(2-x)}}&=3^{3}.3^{x+1}\\ 3^{\frac{-4+2x}{3}}&=3^{3+(x+1)}\\ \displaystyle \frac{-4+2x}{3}&=4+x\\ -4+2x&=12+3x\\ 2x-3x&=12+4\\ -x&=16\\ x&=-16 \end{aligned} \end{array}$