$\begin{array}{ll}\\ 46.&\textrm{Jika diketahui}\: \quad \displaystyle x^{\displaystyle x^{\displaystyle x^{\displaystyle 2}}}=2\\ &\textrm{maka nilai}\quad x^{\displaystyle x^{\displaystyle 2}}+x^{\displaystyle 2}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{2}\sqrt{2}\\ \textrm{b}.&\displaystyle \sqrt{2}\\ \textrm{c}.&\displaystyle 2\\ \textrm{d}.&\displaystyle 2\sqrt{2}\\ \textrm{e}.&\displaystyle 4 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{e}\\ &\textrm{Diketahui bahwa}\quad x^{\displaystyle x^{\displaystyle x^{\displaystyle 2}}}=2,\quad \textrm{maka nilai}\\ &x^{\displaystyle x^{\displaystyle 2}}+x^{\displaystyle 2}=2+2=4\\ &\textrm{perhatikan cara penyelesaiannya pada uraian}\\ &\textrm{jawaban pada nomor soal sebelumnya} \end{array}$.
$\begin{array}{ll}\\ 47.&\textrm{Nilai}\: \quad x\quad \textrm{pada}\quad\displaystyle 9^{\displaystyle 2^{\displaystyle x}}=3^{\displaystyle 8^{\displaystyle x}}\:\: \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 3\\ \textrm{b}.&\displaystyle 1\\ \textrm{c}.&\displaystyle 6\\ \textrm{d}.&\displaystyle \frac{1}{2}\\ \textrm{e}.&\displaystyle \frac{1}{3} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{d}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&9^{\displaystyle 2^{\displaystyle x}}=3^{\displaystyle 8^{\displaystyle x}}\Leftrightarrow \left( 3^{\displaystyle 2} \right)^{\displaystyle 2^{\displaystyle x}}=3^{\displaystyle \left( 2^{\displaystyle 3} \right)^{\displaystyle x}}\\ &\Leftrightarrow 3^{\displaystyle 2^{\displaystyle 1}.2^{\displaystyle x}}=3^{\displaystyle 2^{\displaystyle 3x}}\Leftrightarrow 3^{\displaystyle 2^{\displaystyle (1+x)}}=3^{\displaystyle 2^{\displaystyle 3x}}\\ &\textrm{Selanjutnya pangkatnya tinggal disamakan}\\ &\textrm{yaitu}:\\ & 1+x=3x\Leftrightarrow 2x=1\Leftrightarrow x=\displaystyle \frac{1}{2} \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 48.&\textrm{Nilai}\: \quad x\quad \textrm{pada}\quad\displaystyle (x+2)x^{\displaystyle x^{\displaystyle 2}}=4x^{\displaystyle 4(3-x)}\\ & \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 1\\ \textrm{b}.&\displaystyle 2\\ \textrm{c}.&\displaystyle 3\\ \textrm{d}.&\displaystyle 4\\ \textrm{e}.&\displaystyle 6 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&(x+2)x^{\displaystyle x^{\displaystyle 2}}=4x^{\displaystyle 4(3-x)}\\ &\textrm{kalikan masing-masing ruas dengan}\quad x^{\displaystyle 4x}\\ &\Leftrightarrow (x+2)x^{\displaystyle x^{\displaystyle 2}}.\left( x^{\displaystyle 4x} \right)=4x^{\displaystyle 4(3-x)}.\left( x^{\displaystyle 4x} \right)\\ &\Leftrightarrow (x+2)x^{\displaystyle x^{\displaystyle 2}+4x}=4x^{\displaystyle (12-4x)+4x}\\ &\Leftrightarrow (x+2)x^{\displaystyle x(x+4)}=4x^{\displaystyle 12}\\ &\Leftrightarrow (x+2)x^{\displaystyle x(x+4)}=(2+2)x^{\displaystyle 2(2+4)}\\ &\: \textrm{Jadi},\quad x=2 \end{aligned} \end{array}$.
$\begin{array}{ll}\\ 49.&\textrm{Jika}\: \quad 3^{\displaystyle m}=a,\:\: 3^{\displaystyle n}=b\quad \textrm{maka nilai}\quad x\\ &\textrm{pada persamaan}\quad \displaystyle 9^{\displaystyle m+n}=a^{\displaystyle x}.b^{\displaystyle x}\\ & \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 1\\ \textrm{b}.&\displaystyle 2\\ \textrm{c}.&\displaystyle 3\\ \textrm{d}.&\displaystyle 4\\ \textrm{e}.&\displaystyle 6 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&9^{\displaystyle m+n}=a^{\displaystyle x}.b^{\displaystyle x}\Leftrightarrow \left( 3^{\displaystyle 2} \right)^{\displaystyle m+n}=a^{\displaystyle x}.b^{\displaystyle x}\\ &\Leftrightarrow \left( 3^{\displaystyle 2} \right)^{\displaystyle m+n}=\left( 3^{\displaystyle m} \right)^{\displaystyle x}.\left( 3^{\displaystyle n} \right)^{\displaystyle x}\\ &\Leftrightarrow \left( 3^{\displaystyle 2} \right)^{\displaystyle m+n}=3^{\displaystyle mx+nx}=\left( 3^{\displaystyle x} \right)^{\left( \displaystyle m+n \right)}\\ &\: \textrm{Jadi, nilai}\quad x=2\end{aligned} \end{array}$.
$\begin{array}{ll}\\ 50.&\textrm{Jika}\: \quad x^{\displaystyle x}=\sqrt[\displaystyle 3]{20+14\sqrt{2}}+\sqrt[\displaystyle 3]{20-14\sqrt{2}}\\ & \textrm{maka nilai}\quad x^{\displaystyle 2}+2^{\displaystyle x}\quad\textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle 2+2^{\displaystyle \sqrt{2}}\\ \textrm{b}.&\displaystyle 17\\ \textrm{c}.&\displaystyle 32\\ \textrm{d}.&\displaystyle 8\\ \textrm{e}.&\displaystyle 16 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{d}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&x^{\displaystyle x}=\sqrt[\displaystyle 3]{20+14\sqrt{2}}+\sqrt[\displaystyle 3]{20-14\sqrt{2}}\\ &\Leftrightarrow x^{\displaystyle x}=\sqrt[\displaystyle 3]{\left( 2+\sqrt{2} \right)^{\displaystyle 3}}+\sqrt[\displaystyle 3]{\left( 2-\sqrt{2} \right)^{\displaystyle 3}}\\ &\Leftrightarrow x^{\displaystyle x}=2+\sqrt{2}+2-\sqrt{2}=4=2^{\displaystyle 2}\\ &\textrm{Sehingga nilai}\\ &x^{\displaystyle 2}+2^{\displaystyle x}=2^{\displaystyle 2}+2^{\displaystyle 2}=4+4=8\end{aligned} \end{array}$.
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