Logarithms are the inverses of exponents. They allow us to solve challenging exponential equations, and they are a good excuse to dive deeper into the relationship between a function …

Use the properties of logarithms in order to rewrite a given expression in an equivalent, different form.

Evaluate basic logarithmic expressions by using the fact that a^x=b is equivalent to log_a (b)=x.

Radicals let us work backwards to get a base, but logarithms retrieve the exponent. The logarithmic properties may look new, but they're just the exponential properties in a new notation.

Evaluate advanced logarithmic expressions by using the fact that a^x=b is equivalent to log_a (b)=x.

Khan AcademySign up

Think of it this way -- logarithms are just another way of looking at things. You know that 2^3 is 8, but if you didn't know what power to raise it to, you'd say 2^x is 8.

The graph of y = log 2 x is shown below. Which of the following is the graph of y = 3 log 2 (x 4) ?

Evaluate basic logarithmic expressions by using the fact that a^x=b is equivalent to log_a (b)=x.

Logarithms are the inverses of exponents. They allow us to solve hairy exponential equations, and they are a good excuse to dive deeper into the relationship between a function and its inverse.