Contoh Soal dan Pembahasan Persiapan PHB Gasal Materi Fungsi Eksponensial (Kelas X)

 $\begin{array}{l}\\ 1.& \text{Bentuk sederhana dari}{\displaystyle \frac{a^p.a^q}{a^r}:a^{2r}\text{adalah ... .}}\\ & \begin{array}{l}\\ \text{a}.& a^{p+q-3r}\\ \text{b}.& a^{p+3r-q}\\ \text{c}.& a^{p-2q+r}\\ \text{d}.& a^{p+q+r}\\ \text{e}.& a^{p-3q-r}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \begin{array}{rl}{\displaystyle \frac{a^p.a^q}{a^r}:a^{2r}}& ={\displaystyle \frac{a^p.a^q}{a^r.a^{2r}}}\\ & ={\displaystyle \frac{a^{p+q}}{a^{r+2r}}}\\ & ={\displaystyle \frac{a^{p+q}}{a^{3r}}}\\ & =a^{p+q-3r}\end{array}\end{array}$.

$\begin{array}{l}\\ 2.& \text{Jika}x=\sqrt[3]{5+\sqrt[3]{8}},\text{maka nilai}\\ & x^3\text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 3\\ \text{b}.& 4\\ \text{c}.& 5\\ \text{d}.& 6\\ \text{e}.& 7\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}x& =\sqrt[3]{5+\sqrt[3]{8}}\text{dipangkatkan 3}\\ & \text{masing-masing ruas}\\ x^3& ={\left(\sqrt[3]{5+\sqrt[3]{8}}\right)}^3\\ & =5+\sqrt[3]{8}\\ & =5+\sqrt[3]{2^3}=5+2=7\end{array}\end{array}$.

$\begin{array}{l}\\ 3.& \text{Jika}{4}^a\times 4^b=64\text{dan}{\displaystyle \frac{4^a}{4^b}=16}\\ & \text{maka nilai dari}a:b\text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 5\\ \text{b}.& {\displaystyle \frac{5}{4}}\\ \text{c}.& {\displaystyle \frac{1}{3}}\\ \text{d}.& 3\\ \text{e}.& {\displaystyle \frac{3}{4}}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \begin{array}{rl}& \text{Diketahui}\\ & \bullet 4^a\times 4^b=64\iff 4^{a+b}=4^3\iff a+b=3....(1)\\ & \bullet {\displaystyle \frac{4^a}{4^b}=16\iff 4^{a-b}=4^2\iff a-b=2...........(2)}\\ & \text{Dari persamaan}(1)\mathrm{\&}(2)\text{akan didapatkan}\\ & \begin{array}{|ll|}\hline \begin{array}{lll}a+b& =& 3\\ a-b& =& 2& +\\ 2a& =& 5\\ a& =& {\displaystyle \frac{5}{2}}\end{array}& \begin{array}{rll}a+b& =& 3\\ a-b& =& 2& -\\ 2b& =& 1\\ b& =& {\displaystyle \frac{1}{2}}\end{array}\\ \hline\end{array}\\ & \text{Sehingga nilai}a:b={\displaystyle \frac{a}{b}={\displaystyle \frac{{\displaystyle \frac{5}{2}}}{{\displaystyle \frac{1}{2}}}=5}}\end{array}\end{array}$.

$\begin{array}{l}\\ 4.& (\mathbf{\text{SPMB 2003}})\\ & \text{Jika}a\ne 0,\text{maka nilai}{\displaystyle \frac{(-2a{)}^3(2a{)}^{-\frac{2}{3}}}{{\left(16a^4\right)}^{\frac{1}{3}}}\text{adalah ... .}}\\ & \begin{array}{l}\\ \text{a}.& -2^{2}a\\ \text{b}.& {\displaystyle -2a}\\ \text{c}.& {\displaystyle 2a^2}\\ \text{d}.& 2^{2}a\\ \text{e}.& {\displaystyle -2a^2}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}{\displaystyle \frac{(-2a{)}^3(2a{)}^{-\frac{2}{3}}}{{\left(16a^4\right)}^{\frac{1}{3}}}}& ={\displaystyle \frac{-8a^3}{(2a{)}^{\frac{2}{3}}.{\left(16a^4\right)}^{\frac{1}{3}}}}\\ & =-{\displaystyle \frac{(2a{)}^3}{(2a{)}^{\frac{2}{3}}.(2a{)}^{\frac{4}{3}}}}\\ & =-{\displaystyle \frac{(2a{)}^3}{(2a{)}^{\frac{2}{3}+\frac{4}{3}}}}\\ & =-{\displaystyle \frac{(2a{)}^3}{(2a{)}^2}}\\ & =-(2a{)}^{3-2}\\ & =-2a\end{array}\end{array}$.

$\begin{array}{l}\\ 5.& \text{Bentuk sederhana dari}{\displaystyle \frac{4^{n+3}-4^{n+1}}{4(4^{n-1})}}\\ & \text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 64\\ \text{b}.& 60\\ \text{c}.& 18\\ \text{d}.& 16\\ \text{e}.& 15\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}{\displaystyle \frac{4^{n+3}-4^{n+1}}{4(4^{n-1})}}& ={\displaystyle \frac{4^n{.4}^3-4^n.4}{4.{\displaystyle \frac{4^n}{4}}}}\\ & ={\displaystyle \frac{4^n(64-4)}{4^n}=60}\end{array}\end{array}$.