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

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.
Solve the equation for .
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)

## Try our mobile app

Our app allows students to get instant step-by-step solutions to all kinds of math troubles.

Scroll to top