$\begin{array}{ll}\\ 41.&\textrm{Nilai}\: \: x\quad \textrm{jika}\quad x^{\displaystyle x^{\displaystyle 16}}=\sqrt[\displaystyle 8]{\displaystyle 2}\quad \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\sqrt[\displaystyle 4]{2}\\ \textrm{b}.&\displaystyle \sqrt[\displaystyle 8]{2}\\ \textrm{c}.&\displaystyle \sqrt{32}\\ \textrm{d}.&\displaystyle \sqrt{8}\\ \textrm{e}.&\sqrt[\displaystyle 16]{2} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{e}\\ &\textrm{Diketahui bahwa}\quad x^{\displaystyle x^{\displaystyle 16}}=\sqrt[\displaystyle 8]{\displaystyle 2}\:=\left( \displaystyle 2 \right)^{\displaystyle \frac{1}{8}}=2^{\displaystyle \frac{2}{16}}.\\ &\textrm{Perhatikan bahwa dengan memangkatkan 16}\\ &\textrm{di masing-masing ruas kita akan mendapatkan}\\ &\begin{aligned}&\left( x^{\displaystyle x^{\displaystyle 16}} \right)^{\displaystyle 16}=\left( \left( \displaystyle 2 \right)^{\displaystyle \frac{2}{16}} \right)^{\displaystyle 16}\\ &\Leftrightarrow x^{\displaystyle 16.x^{\displaystyle 16}}=\left( \displaystyle 2 \right)^{\left( \displaystyle 2 \right)}\\ &\Leftrightarrow \left( x^{\displaystyle 16} \right)^{\displaystyle x^{\displaystyle 16}}=\left( \displaystyle 2 \right)^{\left( \displaystyle 2 \right)}\\ &\Leftrightarrow x^{\displaystyle 16}=\displaystyle 2\Leftrightarrow x=\sqrt[\displaystyle 16]{2} \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 42.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle x^{\displaystyle x+1}}=2^{\displaystyle -2^{\displaystyle -\frac{3}{2}}}\\ &\textrm{maka nilai}\quad x+1\quad \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{3}{2}\\ \textrm{b}.&\displaystyle \frac{2}{3}\\ \textrm{c}.&\displaystyle \frac{4}{3}\\ \textrm{d}.&\displaystyle \frac{1}{3}\\ \textrm{e}.&\displaystyle \frac{1}{2} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{a}\\ &\textrm{Diketahui bahwa}\\ &\begin{aligned}&\displaystyle x^{\displaystyle x^{\displaystyle x+1}}=2^{\displaystyle -2^{\displaystyle -\frac{3}{2}}}\\ &\Leftrightarrow \displaystyle x^{\displaystyle x^{\displaystyle x+1}}=\left( \displaystyle \frac{1}{2} \right)^{\displaystyle \left( \displaystyle \frac{1}{2} \right)^{\displaystyle \frac{3}{2}}}\\ &\Leftrightarrow \displaystyle x^{\displaystyle x^{\displaystyle x+1}}=\left( \displaystyle \frac{1}{2} \right)^{\displaystyle \left( \displaystyle \frac{1}{2} \right)^{\left( \displaystyle \frac{1}{2}+1 \right)}}\\ &\textrm{Sehingga nilai dari}\\ &x+1=\displaystyle \frac{1}{2}+1=\frac{3}{2} \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 43.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle -x^{\displaystyle 1-x}}=3^{\displaystyle 18}\\ &\textrm{maka nilai}\quad x\displaystyle ^{\displaystyle x}\quad \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{3}\\ \textrm{b}.&\displaystyle -\frac{1}{3}\\ \textrm{c}.&\displaystyle \frac{1}{9}\\ \textrm{d}.&\displaystyle -\frac{1}{9}\\ \textrm{e}.&\displaystyle \frac{1}{27} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Diketahui bahwa}\\ &\begin{aligned}&\displaystyle x^{\displaystyle -x^{\displaystyle 1-x}}=3^{\displaystyle 18}\Leftrightarrow x^{\displaystyle -x^{\displaystyle 1}.x^{\displaystyle -x}}=3^{\displaystyle 2.9}\\ &\Leftrightarrow x^{\displaystyle -x.x^{\displaystyle -x}}=3^{\displaystyle 2.3^{\displaystyle 2}}\\ &\Leftrightarrow \left( x^{\displaystyle -x} \right)^{\displaystyle \left( x^{\displaystyle -x} \right)}=\left( 3^{\displaystyle 2} \right)^{\left( \displaystyle 3^{\displaystyle 2} \right)}\\ &\textrm{Sehingga kita mendapatkan persamaan}\\ &x^{\displaystyle -x}=3^{\displaystyle 2}\\ &\textrm{Selanjutnya pangkatkan -1 masing-masing ruas}\\ & \left( x^{\displaystyle -x} \right)^{\displaystyle -1}=\left( 3^{\displaystyle 2} \right)^{\displaystyle -1}\Leftrightarrow x^{\displaystyle x}=\displaystyle \frac{1}{3^{\displaystyle 2}}=\displaystyle \frac{1}{9} \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 44.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle x^{\displaystyle x}}=2\\ &\textrm{maka nilai}\quad x\displaystyle ^{\displaystyle x^{\displaystyle x}+x^{\displaystyle x+x^{\displaystyle x+x^{\displaystyle x}}}}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 8\\ \textrm{b}.&\displaystyle 16\\ \textrm{c}.&\displaystyle 32\\ \textrm{d}.&\displaystyle 48\\ \textrm{e}.&\displaystyle 81 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}& x\displaystyle ^{\displaystyle x^{\displaystyle x}+x^{\displaystyle x+x^{\displaystyle x+x^{\displaystyle x}}}}\\ &=x^{\displaystyle x^{\displaystyle x}}.x^{\displaystyle x^{\displaystyle x}.x^{\displaystyle x^{\displaystyle x}.x^{\displaystyle x^{\displaystyle x}}}}\\ &=2.\left( 2^{\displaystyle 2^{\displaystyle 2}} \right)=2.\left( 2^{\displaystyle 4} \right)=2.16=32 \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 45.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=3\\ &\textrm{maka nilai}\quad x^{\displaystyle 3}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{3}\sqrt{3}\\ \textrm{b}.&\displaystyle \sqrt{3}\\ \textrm{c}.&\displaystyle 3\\ \textrm{d}.&\displaystyle 3\sqrt{3}\\ \textrm{e}.&\displaystyle 27 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=3\\ &\Leftrightarrow x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle \left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}}\\ &\Leftrightarrow x^{\displaystyle x^{\displaystyle x^{\displaystyle 3}}}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle \left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle \left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}}}\\ &\Leftrightarrow x=\sqrt[\displaystyle 3]{3},\quad \textrm{maka nilai}\quad x^{\displaystyle 3}=\left( \sqrt[\displaystyle 3]{3} \right)^{\displaystyle 3}=3 \end{aligned} \end{array}$.
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