Convert the exponential equations to logarithmic notation: e) 50 = 1, g) 125 = (1/5)⁻³

Here, the base $b=5$, the exponent $x=0$, and the result $y=1$.

Using the rule $\log_b y = x$, we get:

The student's attempt $\log 5 = 1$ is incorrect because it implies $10^1 = 5$, which is false. The correct base for the logarithm should be 5, and the result of the logarithm is the exponent, 0.
The final answer is $\boxed{\log_5 1 = 0}$.

Here, the base $b=\frac{1}{5}$, the exponent $x=-3$, and the result $y=125$.

Using the rule $\log_b y = x$, we get:

The final answer is $\boxed{\log_{\frac{1}{5}} 125 = -3}$.