Question - Logarithmic Equation Problem Solving
Solution:
\[
\begin{align*}
\log_7(7^{2y} - 18) & = y + 1 \\
7^{2y} - 18 & = 7^{y+1} \\
7^{2y} - 7^{y}7 - 18 & = 0 \\
\text{令 } z = 7^{y}, \text{得到} \\
z^{2} - 7z - 18 & = 0 \\
(z - 9)(z + 2) & = 0 \\
z = 9 \text{ 或 } z = -2, & \text{但是} z = 7^{y} > 0, \text{所以不考虑} z = -2. \\
7^{y} & = 9 \\
y & = \log_7 9
\end{align*}
\]
所以正确答案是 \( C. \log_7 9 \).
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