Can someone help me with this Math Problem?

Question

Evaluate the expression. Without using a calculator.
Log script 9 9 ^-0.56

Answer 1

log base 9 and 9^x are inverse functions, so the answer is:
-0.56

log[base b] (x) means "that exponent that when raised upon the base b returns x".

So in your case, it is saying what is "that exponent when raised upon the base 9 gives 9^-0.56?".

Well obviously that would be.
-0.56

It's kind of like saying what is the square root of x²?
Or what is 10 * (x/10)?

The log and exponent operations (on the same base) undo each other.

Answer 2

as per log rules, log of any number to the base of same number is 1

ex: log_b(b) = log(b/b) = 1

similarly log_9[9 ^-(0.56)]

=>-0.56[log(9)/log(9)] = -0.56