Write the logarithmic expression as a single logarithm with coefficient 1 , and simplify as much as possible. Assume that the variables represent positive real numbers.
\[
9 \log _{2} x-8 \log _{2} y-3 \log _{2} z=\square
\]
\begin{tabular}{ccc}
$\log _{a}$ & 믐 & $\square^{\square}$ \\
$x$ & 5
\end{tabular}
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Answer
Final Answer: \( \boxed{\log _{2} \left(\frac{x^9}{y^8 \cdot z^3}\right)} \)
Step 1 ：Applying the power rule to the logarithmic expression, we get: \( \log _{2} x^9 - \log _{2} y^8 - \log _{2} z^3 \)
Step 2 ：Now, we can apply the quotient rule to combine these logarithms into a single logarithm: \( \log _{2} \left(\frac{x^9}{y^8 \cdot z^3}\right) \)
Step 3 ：So, the simplified expression is \( \log _{2} \left(\frac{x^9}{y^8 \cdot z^3}\right) \)
Step 4 ：Final Answer: \( \boxed{\log _{2} \left(\frac{x^9}{y^8 \cdot z^3}\right)} \)
