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:

Log_{2}(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 2^{3}=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 log_{10}100=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_{e}1=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 e^{0}=1, or x=0.

Ln(x)=log_{e}(x)