Use the properties of logarithms to expand $\log \frac{z^{7}}{y}$ .
Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive.

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The expanded form of $\log \frac{z^{7}}{y}$ is $- \log y + 7 \log z$ .

Steps

Step 1 ：Given the expression $\log \frac{z^{7}}{y}$ .

Step 2 ：Use the properties of logarithms to expand the expression. The properties of logarithms state that $\log \frac{a}{b} = \log a - \log b$ and $\log a^{n} = n \log a$ .

Step 3 ：Applying these properties, the expression $\log \frac{z^{7}}{y}$ can be expanded to $- \log y + 7 \log z$ .

Step 4 ：Final Answer: The expanded form of $\log \frac{z^{7}}{y}$ is $- \log y + 7 \log z$ .

Use the properties of logarithms to expand log⁡z7y.Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive.

Answer

Popular Problems

Use the properties of logarithms to expand $\log \frac{z^{7}}{y}$ .
Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive.