Answer:



Explanation:
We can express the given logarithmic expressions in terms of x, y, z or w by using the laws of logarithms.

Part (a)

By using the log product law, we can express log₇(xz) as:


Part (b)

By using the log quotient law, we can express log₇(y/x) as:


Part (c)

By using the log power law, we can express log₇(∛z) as:
![\begin{aligned}\log_7 \left(\sqrt[3]{z}\right)&=\log_7 \left(z^{(1)/(3)\right) \\&=(1)/(3)\log_7(z)\end{aligned}](https://img.qammunity.org/2024/formulas/mathematics/college/clctky8iolw2y0jkki9ryh52z6q8h7zaro.png)