Convert 5^m = 64 to logarithmic form?

Question

Also, can you tell how to use a calculator  to find the answer?

Answer 1

5^m=64.

Take logs to base 5: m=log₅(64)=2.584

OR

Take logs to a different base, e.g., natural logs:

mln(5)=ln(64), m=ln(64)/ln(5)=4.1589/1.6094=2.584.

If you have a scientific calculator with natural logs on it, you should be able to use the second method. Some calculators allow you to find logs to any base. It doesn’t matter which base you use, the answer will be the same.