Use properties of logarithms to rewrite the given expression as the logarithm of a single quantity, then enter that single quantity in the answer box to complete the expression.
\[
\frac{1}{4} \log (x)-5 \log (y)-3 \log (z)
\]
Answer
Finally, we simplify the expression inside the logarithm to get the final answer. The expression \(\frac{x^{\frac{1}{4}}}{y^5 z^3}\) simplifies to \(\boxed{\frac{\sqrt[4]{x}}{y^5 z^3}}\).
Step 1 ：First, we apply the power rule of logarithms, which states that \(\log_b(m^n) = n \log_b(m)\), to the given expression. This gives us \(\log (x^{\frac{1}{4}})-\log (y^5)-\log (z^3)\).
Step 2 ：Next, we apply the quotient rule of logarithms, which states that \(\log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right)\), to the expression. This gives us \(\log \left(\frac{x^{\frac{1}{4}}}{y^5 z^3}\right)\).
Step 3 ：Finally, we simplify the expression inside the logarithm to get the final answer. The expression \(\frac{x^{\frac{1}{4}}}{y^5 z^3}\) simplifies to \(\boxed{\frac{\sqrt[4]{x}}{y^5 z^3}}\).
