# Precalculus Examples

Solve for x log base 3 of 4x-9=2
Step 1
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 2
Solve for .
Step 2.1
Rewrite the equation as .
Step 2.2
Raise to the power of .
Step 2.3
Move all terms not containing to the right side of the equation.
Step 2.3.1
Add to both sides of the equation.
Step 2.3.2
Step 2.4
Divide each term in by and simplify.
Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Cancel the common factor of .
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Cancel the common factor of and .
Step 2.4.3.1.1
Factor out of .
Step 2.4.3.1.2
Cancel the common factors.
Step 2.4.3.1.2.1
Factor out of .
Step 2.4.3.1.2.2
Cancel the common factor.
Step 2.4.3.1.2.3
Rewrite the expression.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: