Take the log of both sides of the equation.

Expand by moving outside the logarithm.

Expand by moving outside the logarithm.

Simplify .

Apply the distributive property.

Multiply by .

Apply the distributive property.

Subtract from both sides of the equation.

Subtract from both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Simplify each term.

Move the negative in front of the fraction.

Move the negative in front of the fraction.

Simplify terms.

Combine the numerators over the common denominator.

Factor out of .

Factor out of .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for m 5^(2m+1)=3^(5m-2)