Solve for $x$ :
\[
\begin{array}{l}
\frac{9}{8} \log _{5} x=-7 \\
x=
\end{array}
\]

Answer

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Answer

Final Answer: The solution to the equation is $x = \boxed{4.475621035299599 \times 10^{-5}}$.

Steps

Step 1 ：The given equation is $\frac{9}{8} \log _{5} x=-7$.

Step 2 ：To solve for $x$, we need to convert the logarithmic equation into an exponential equation.

Step 3 ：The base of the logarithm is 5, so we can rewrite the equation as $5$ raised to the power of the right side of the equation equals $x$.

Step 4 ：By doing this, we get $x = 5^{-\frac{7}{\frac{9}{8}}}$.

Step 5 ：Solving this, we get $x = 4.475621035299599 \times 10^{-5}$.

Step 6 ：Final Answer: The solution to the equation is $x = \boxed{4.475621035299599 \times 10^{-5}}$.