Solve the following equation for x: X=logx 1

Question

I need help answering this question that will be on my test tomorrow

Answer 1

Note that b = log[base c] d is the same as c^b = d

Thus, we have:

x = log[base x] 1
x^x = 1
ln (x^x) = ln (1)
x * ln (x) = 0
x = 0 or ln (x) = 0
x = 0 or x = 1

Note that we cannot possible have log[base 0] 1.
Thus, the only possible answer is 1.