EKSPONEN-ANEKA CONTOH SOAL LANJUTAN (BAGIAN 9)

 $\begin{array}{ll}\\ 41.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle x^{\displaystyle x}}=2\\ &\textrm{maka nilai}\quad x\displaystyle ^{\displaystyle x^{\displaystyle x}+x^{\displaystyle x+x^{\displaystyle x+x^{\displaystyle x}}}}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 8\\ \textrm{b}.&\displaystyle 16\\ \textrm{c}.&\displaystyle 32\\ \textrm{d}.&\displaystyle 48\\ \textrm{e}.&\displaystyle 81 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}& x\displaystyle ^{\displaystyle x^{\displaystyle x}+x^{\displaystyle x+x^{\displaystyle x+x^{\displaystyle x}}}}\\ &=x^{\displaystyle x^{\displaystyle x}}.x^{\displaystyle x^{\displaystyle x}.x^{\displaystyle x^{\displaystyle x}.x^{\displaystyle x^{\displaystyle x}}}}\\ &=2.\left( 2^{\displaystyle 2^{\displaystyle 2}} \right)=2.\left( 2^{\displaystyle 4} \right)=2.16=32 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 42.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=3\\ &\textrm{maka nilai}\quad x^{\displaystyle 3}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{3}\sqrt{3}\\ \textrm{b}.&\displaystyle \sqrt{3}\\ \textrm{c}.&\displaystyle 3\\ \textrm{d}.&\displaystyle 3\sqrt{3}\\ \textrm{e}.&\displaystyle 27 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=3\\ &\Leftrightarrow x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle \left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}}\\ &\Leftrightarrow x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle \left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle \left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}}}\\ &\Leftrightarrow x=\sqrt[\displaystyle 3]{3},\quad \textrm{maka nilai}\quad x^{\displaystyle 3}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}=3  \end{aligned} \end{array}$.