EKSPONEN-ANEKA CONTOH SOAL LANJUTAN (BAGIAN 10)

 $\begin{array}{ll}\\ 46.&\textrm{Nilai}\: \quad x\quad \textrm{pada}\quad\displaystyle 9^{\displaystyle 2^{\displaystyle x}}=3^{\displaystyle 8^{\displaystyle x}}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 3\\ \textrm{b}.&\displaystyle 1\\ \textrm{c}.&\displaystyle 6\\ \textrm{d}.&\displaystyle \frac{1}{2}\\ \textrm{e}.&\displaystyle \frac{1}{3} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{d}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&9^{\displaystyle 2^{\displaystyle x}}=3^{\displaystyle 8^{\displaystyle x}}\Leftrightarrow \left( 3^{\displaystyle 2} \right)^{\displaystyle 2^{\displaystyle x}}=3^{\displaystyle \left( 2^{\displaystyle 3} \right)^{\displaystyle x}}\\ &\Leftrightarrow 3^{\displaystyle 2^{\displaystyle 1}.2^{\displaystyle x}}=3^{\displaystyle 2^{\displaystyle 3x}}\Leftrightarrow 3^{\displaystyle 2^{\displaystyle (1+x)}}=3^{\displaystyle 2^{\displaystyle 3x}}\\ &\textrm{Selanjutnya pangkatnya tinggal disamakan}\\ &\textrm{yaitu}:\\ & 1+x=3x\Leftrightarrow 2x=1\Leftrightarrow x=\displaystyle \frac{1}{2} \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 47.&\textrm{Nilai}\: \quad x\quad \textrm{pada}\quad\displaystyle (x+2)x^{\displaystyle x^{\displaystyle 2}}=4x^{\displaystyle 4(3-x)}\\ & \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 1\\ \textrm{b}.&\displaystyle 2\\ \textrm{c}.&\displaystyle 3\\ \textrm{d}.&\displaystyle 4\\ \textrm{e}.&\displaystyle 6 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&(x+2)x^{\displaystyle x^{\displaystyle 2}}=4x^{\displaystyle 4(3-x)}\\ &\textrm{kalikan masing-masing ruas dengan}\quad x^{\displaystyle 4x}\\ &\Leftrightarrow (x+2)x^{\displaystyle x^{\displaystyle 2}}.\left( x^{\displaystyle 4x} \right)=4x^{\displaystyle 4(3-x)}.\left( x^{\displaystyle 4x} \right)\\ &\Leftrightarrow (x+2)x^{\displaystyle x^{\displaystyle 2}+4x}=4x^{\displaystyle (12-4x)+4x}\\ &\Leftrightarrow (x+2)x^{\displaystyle x(x+4)}=4x^{\displaystyle 12}\\ &\Leftrightarrow (x+2)x^{\displaystyle x(x+4)}=(2+2)x^{\displaystyle 2(2+4)}\\ &\: \textrm{Jadi},\quad x=2 \end{aligned} \end{array}$.