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 3x + 4x = 7x
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 3x + 4x and graph 7x meet at (1, 7)
so x = 1 is the solution of the exponential equation