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)`

Step-by-step 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=(\ln 7)/(4\ln 7-5\ln 3) \end{gathered}`

So value of x is,

`x=(\ln 7)/(4\ln 7-5\ln 3)`