# How to Solve the Exponential Equation 3^x + 4^x = 7^x

## Algebra Math Problem

Solve for natural solution for *x* from the exponential equation 3^{x} + 4^{x} = 7^{x}

## Solving the exponential equation

\begin{aligned} & 3^x+4^x=7^x \\ \\ & \dfrac{3^x}{7^x}+\dfrac{4^x}{7^x}=1\\ \\ & \bigg(\dfrac{3}{7}\bigg)^x+\bigg(\dfrac{4}{7}\bigg)^x=1\\ \end{aligned}

From the above equation ** x = 1** is the only real solution

## Graphical solution of this exponential equation

From graph 3^{x} + 4^{x} and graph 7^{x} meet at (1, 7)

so** x = 1 **is the solution of the exponential equation