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