Using Natural Log and Log-Base-10

For any equation , . Thus, we are trying to determine what power of 10 is 1000. , so our answer is 3.

is equivalent to . In this case, you know the value of (the argument of a logarithmic equation) and b (the answer to the logarithmic equation). You must find a solution for the base.

Most of us don't know what the exponent would be if and unfortunately there is no on a graphing calculator -- only (which stands for ).

Fortunately we can use the base change rule:

Plug in our given values.