Help with logarithms?

Question

please help me understand how to solve this:

evaluate log7^49 without a calculator

Answer 1

If you mean

log[base 7](49), the answer is 2. Here's how you solve it.

Let x = log[base 7](49). Convert this to logarithmic form, and we get

7^x = 49

49 is equal to 7^2, so we can express it as 7^2.

7^x = 7^2

Now we have the same base but different exponents. We can equate the powers.

x = 2

Answer 2

x = log(7)(49)
7^x = 49
7^x = 7^2
x = 2

the other way to do it is

log(7)(49) = log(49)/log(7), but you would need a calculator to be sure.