Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .

Raise to the power of .

Rewrite the equation as .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Solve for x log base 5 of 3x+1=2