Meaning of Logarithms

Logarithms are the inverse functions of exponential functions. They help us solve for an exponent.

If I have log_{b}(c), this is read “log base b of c.”

The base b is the same base as the base of an exponent. The answer you get when you evaluate this is the same as the exponent. The relationship between between a log and an exponent is the same as the relationship between division and multiplication.

    \[log_{3}(81)=4 \longleftrightarrow 3^4=81\]

and

    \[log_{10}(100)=2 \longleftrightarrow 10^2=100\]

 

Evaluating (easy) Logarithms

Evaluating logarithms is just about finding the number that would make the exponent work.

log_{3}(9)= (3 to what power is 9?)

 

Common Logs & Natural Logs

Most logarithms, like the ones on your calculator, are either log_{10}, written simply as log, or log_{e}, written as ln. log_{10} is called common log, and ln is called a natural log. Most calculators have buttons for common logs and natural logs, but not any other type of log.