A logarithmic function is the inverse of an exponential function. It is used to find the exponent to which a base number must be raised to produce a given value. The general form of a logarithmic function is: f(x)=logb​(x)

Common logarithms are logarithms with a base of 10

-not necessary to write the base

-logx is the same as log10x

An exponential function is a function in the form f(x) = b^x, where “x” is a variable and “b” is a constant which is called the base of the function such that b ≠0, 1

First differences are related by multiplication

when |b|>1, exponential functions increasing (growth)

when |b|<1, exponential functions decreasing (decay)

Power law: log_amⁿ = n · log_am

where a > 0, a ≠ 0, m > 0, n ∈ R

Change of base formula: Log_nm = log m/log n

where n > 0, n ≠ 1, m > 0