A not so helpful definition of logarithms from 1797 Britannica:

Logarithms are another way to consider unknown exponents. They ask: To what exponent do we raise this base to get another number?

Here are a few examples and explanations:

Log₂(8) = x

We interpret this as asking: “What number do we raise 2 to, to get 8”. So, let’s convert this into exponential form: 2^x=8. We know that 2*2*2=8 so 2³=8. Thus, x=3.

If a problem simply has log without a base, it is assumed that the base is 10. Thus: log 100=x is the same as log₁₀100=x. In exponential form: 10^x=100, thus x=2.

If we see a problem including ln (1)=x, it means the same thing as log_e1=x. So, converting to exponential form, e^x=1. “e” is just a number, 2.71…. that goes on forever and is on most calculators. We know that any number raised to the 0 power is 1, so e⁰=1, or x=0.

Ln(x)=log_e(x)