the Given:
The equation is,
[tex]7^{4x-1}=3^{5x}[/tex]
Explanation:
Take a natural log on both sides of the equation and simplify it.
[tex]\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}[/tex]
So value of x is,
[tex]x=\frac{\ln 7}{4\ln 7-5\ln 3}[/tex]
