Determine whether the following statements are true and give an explanation or counterexample.

a. If y = 3^x, then x = ³√y.

b. log_b x/log_b y = log_b x - log_b y

c. log₅ 4⁶ = 4 log₅ 6

d. 2 = 10^{log10 2}

e. 2 = ln 2^e

f. If f(x) = x² + 1, then f^-1(x) = 1/(x² + 1).

g. If f(x) = 1/x, then f^-1(x) = 1/x.