Question

In calculus early transcendental functions Can I solve for x if the base number isn’t the same? 7^4x-1=3^5x

Answer 1

the Given:

The equation is,

$7^{4x-1}=3^{5x}$

Explanation:

Take a natural log on both sides of the equation and simplify it.

$\begin{gathered} \ln (7^{4x-1})=\ln (3^{5x}) \\ (4x-1)\ln 7=5x\ln 3 \\ 4x\ln 7-\ln 7=5x\ln 3 \\ 4x\ln 7-5x\ln 3=\ln 7 \\ x(4\ln 7-5\ln 3)=\ln 7 \\ x=\frac{\ln 7}{4\ln 7-5\ln 3} \end{gathered}$

So value of x is,

$x=\frac{\ln 7}{4\ln 7-5\ln 3}$