Lanjutan 1 Contoh Soal dan Pembahasan Persiapan PHB Gasal Materi Fungsi Eksponensial (Kelas X)

$\begin{array}{l}\\ 6.& \text{Bentuk sederhana dari}\\ & {\left({\displaystyle \frac{1}{2}}\right)}^{-{\left(\frac{1}{2}\right)}^{-1}}+{\left({\displaystyle \frac{1}{3}}\right)}^{-{\left(\frac{1}{3}\right)}^{-1}}+{\left({\displaystyle \frac{1}{4}}\right)}^{-{\left(\frac{1}{4}\right)}^{-1}}+{\left({\displaystyle \frac{1}{5}}\right)}^{-{\left(\frac{1}{5}\right)}^{-1}}\\ & \text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 3142\\ \text{b}.& 287\\ \text{c}.& 3412\\ \text{d}.& 4116\\ \text{e}.& 4096\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}& {\left({\displaystyle \frac{1}{2}}\right)}^{-{\left(\frac{1}{2}\right)}^{-1}}+{\left({\displaystyle \frac{1}{3}}\right)}^{-{\left(\frac{1}{3}\right)}^{-1}}+{\left({\displaystyle \frac{1}{4}}\right)}^{-{\left(\frac{1}{4}\right)}^{-1}}+{\left({\displaystyle \frac{1}{5}}\right)}^{-{\left(\frac{1}{5}\right)}^{-1}}\\ & ={\left({\displaystyle \frac{1}{2}}\right)}^{-2}+{\left({\displaystyle \frac{1}{3}}\right)}^{-3}+{\left({\displaystyle \frac{1}{4}}\right)}^{-4}+{\left({\displaystyle \frac{1}{5}}\right)}^{-5}\\ & =2^2+3^3+4^4+5^5\\ & =4+27+256+3125\\ & =3412\end{array}\end{array}$.

$\begin{array}{l}\\ 7.& \text{Nilai dari}\\ & \underset{89}{\underbrace{(-7)(-7)(-7)\cdots (-7)}}-(-7{)}^{89}\\ & \text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 2\\ \text{b}.& 7\\ \text{c}.& 4\\ \text{d}.& 0\\ \text{e}.& 9\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}& \underset{89}{\underbrace{(-7)(-7)(-7)\cdots (-7)}}-(-7{)}^{89}\\ & =(-7{)}^{89}-(-7{)}^{89}\\ & =0\end{array}\end{array}$.

$\begin{array}{l}\\ 8.& \text{Nilai dari}{\left(\sqrt{3\times \sqrt[4]{27\times \sqrt[3]{81}}}\right)}^{{\displaystyle \frac{24}{25}}}\\ & \text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 1\\ \text{b}.& 2\\ \text{c}.& 3\\ \text{d}.& 4\\ \text{e}.& 5\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}& {\left(\sqrt{3\times \sqrt[4]{27\times \sqrt[3]{81}}}\right)}^{{\displaystyle \frac{24}{25}}}\\ & ={(3^{\frac{1}{2}}.(3^3{)}^{\frac{1}{2.4}}.(3^4{)}^{\frac{1}{2.4.3}})}^{{\displaystyle \frac{24}{25}}}\\ & ={\left(3^{\frac{1}{2}+\frac{3}{8}+\frac{4}{24}}\right)}^{{\displaystyle \frac{24}{25}}}\\ & =3^{\frac{12}{25}+\frac{9}{25}+\frac{4}{25}}\\ & =3^{\frac{25}{25}}\\ & =3\end{array}\end{array}$.

$\begin{array}{l}\\ 9.& \text{Jika}\sqrt{{27}^{2x+3}}={\displaystyle \frac{1}{3^{x-2}{.9}^{3x}},\text{maka nilai}}\\ & 8x+2\text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 0\\ \text{b}.& 2\\ \text{c}.& 4\\ \text{d}.& 8\\ \text{e}.& 12\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{a}}\\ & \mathbf{\text{Alternatif 1}}\\ & \begin{array}{rl}\sqrt{{27}^{2x+3}}& ={\displaystyle \frac{1}{3^{x-2}{.9}^{3x}}}\\ {27}^{{\displaystyle \frac{2x+3}{2}}}& =3^{-(x-2)}{.9}^{-3x}\\ 3^{3.\left({\displaystyle \frac{2x+3}{2}}\right)}& =3^{2-x}{.3}^{2(-3x)}\\ 3^{3.\left({\displaystyle \frac{2x+3}{2}}\right)}& =3^{2-x-6x}\\ 3{}^{3.\left({\displaystyle \frac{2x+3}{2}}\right)}& =3{}^{2-7x}\\ 3\frac{(2x+3)}{2}& =2-7x\\ 6x+9& =4-14x\\ 6x+14x& =4-9\\ 20x& =-5\\ & x=-{\displaystyle \frac{1}{4}}\\ \text{maka nilai}& \\ 8x+2& =8(-{\displaystyle \frac{1}{4}})+2=-2+2=0\end{array}\\ & \mathbf{\text{Alternatif 2}}\\ & \begin{array}{rl}\sqrt{{27}^{2x+3}}& ={\displaystyle \frac{1}{3^{x-2}{.9}^{3x}}}\\ {27}^{{\displaystyle \frac{2x+3}{2}}}{.3}^{x-2}{.9}^{3x}& =1\\ 3^{3\left({\displaystyle \frac{2x+3}{2}}\right)}{.3}^{x-2}{.3}^{2(3x)}& =3^0\\ 3^{3\left({\displaystyle \frac{2x+3}{2}}\right)+x-2+6x}& =3^0\\ {\displaystyle \frac{3(2x+3)}{2}+7x-2}& =0\\ 6x+9+14x-4& =0\\ 20x+5& =0\\ 20x& =-5\\ x& =-{\displaystyle \frac{1}{4}}\\ \text{Selanjutnya sama}& \\ \text{dengan langkah no.1}& \text{di atas}\end{array}\end{array}$.

$\begin{array}{l}\\ 10.& \text{Penyelesaian persamaan}{3}^{2x+1}={81}^{x-2}\\ & \text{adalah ... .}\\ & \begin{array}{l}\\ \text{a}.& 0\\ \text{b}.& 2\\ \text{c}.& 4\\ \text{d}.& 4{\displaystyle \frac{1}{2}}\\ \text{e}.& 16\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}{3}^{2x+1}& ={81}^{x-2}\\ 3^{2x+1}& =(3^4{)}^{x-2}\\ 3^{2x+1}& =3^{4x-8}\\ 2x+1& =4x-8\\ 2x-4x& =-8-1\\ -2x& =-9\\ x& ={\displaystyle \frac{-9}{-2}}\\ & =4{\displaystyle \frac{1}{2}}\end{array}\end{array}$.