need help with logarithms (Please Provide Explanation)?

Question

log (base=a) (argument=a) (exponent of argument=x)
and a^(log (base=a) (argument=x)

What are the restrictions on "a" and "x"?

if you're not sure with the terminology:
ex. log x ---> base=10 argument=x

WHAT ARE THE RESTRICTIONS of "x" and "a"?????

Answer 1

log_a (a^x) = x

a^[log_a(x)] = x

The base of a log (in this case we are talking about the variable a) has to be positive and not equal to 1.
x can be anything.

Also, you can only take the log of positive numbers.

Answer 2

log(a)a^x = xlog(a)a