Nilai yang memenuhi persamaan \(^3 \log \{^2 \log [1 + \: ^2 \log (x - 1)]\} = 0\) adalah \(p\). Nilai dari \(2^p + 2\) adalah ...
Jawab: C
Menyelesaikan persamaan
\begin{equation*}
\begin{split}
^3 \log \{^2 \log [1 + \: ^2 \log (x - 1)]\} &= 0\\\\
\cancel{^3 \log} \{^2 \log [1 + \: ^2 \log (x - 1)]\} &= \cancel{^3 \log} 1\\\\
^2 \log [1 + \: ^2 \log (x - 1)] &= 1\\\\
\cancel{^2 \log} [1 + \: ^2 \log (x - 1)] &= \cancel{^2 \log} 2\\\\
1 + \: ^2 \log (x - 1) &= 2\\\\
^2 \log (x - 1) &= 1\\\\
\cancel{^2 \log} (x - 1) &= \cancel{^2 \log} 2\\\\
x - 1 &= 2\\\\
x &= 3
\end{split}
\end{equation*}
Syarat terdefinisi
\(x - 1 = 3 - 1 = 2 \: {\color {blue} > 0 \quad \text{ OK!}}\)
HP = {3}
Maka \(2^p + 2 = 2^3 + 2 = 10\)