Take the log of both sides of the equation.

Rewrite as .

Expand by moving outside the logarithm.

Rewrite as .

Expand by moving outside the logarithm.

Simplify each term.

Simplify by moving inside the logarithm.

Raise to the power of .

Move all the terms containing a logarithm to the left side of the equation.

Use the quotient property of logarithms, .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Subtract from both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x 100(1.05)^x=200(1.09)^(3x)