The change of base rule can be used if and are greater than and not equal to , and is greater than .

Substitute in values for the variables in the change of base formula, using .

Rewrite as an equation.

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and does not equal , then is equivalent to .

Create equivalent expressions in the equation that all have equal bases.

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

The variable is equal to .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate log base 0.1 of 100