One number or word is missing in the statement.
Assume you mean "what is the log base 4 of 64?"
That is:
Since, logarithm is the inverse function of exponential, another way to say that is to what exponent must be raised 4 to make 64?
This is, find x such that 4 ˣ = 64
Since 64 is 4³, the answer would be 3.
If the question were "what is the log base 2 of 64?" then other way to say it is to what number must be raised 2 to make 64?
And the answer is found making:
2ˣ = 64
2ˣ = 2⁶
Therefore, x = 6.
Assume you mean "what is the log base 4 of 64?"
That is:
Since, logarithm is the inverse function of exponential, another way to say that is to what exponent must be raised 4 to make 64?
This is, find x such that 4 ˣ = 64
Since 64 is 4³, the answer would be 3.
If the question were "what is the log base 2 of 64?" then other way to say it is to what number must be raised 2 to make 64?
And the answer is found making:
2ˣ = 64
2ˣ = 2⁶
Therefore, x = 6.