Question

3^2x= 5^x-1

Answer 1

\[\Large 3^{2x} = 5^{x-1}\]


\[\Large \ln\left(3^{2x}\right) = \ln\left(5^{x-1}\right)\]


\[\Large 2x\ln\left(3\right) = (x-1)\ln\left(5\right)\]


\[\Large 2x\ln\left(3\right) = x\ln\left(5\right)-\ln\left(5\right)\]


\[\Large 2x\ln\left(3\right)-x\ln\left(5\right) = -\ln\left(5\right)\]


\[\Large x\left(2\ln\left(3\right)-\ln\left(5\right)\right) = -\ln\left(5\right)\]


\[\Large x = \frac{-\ln\left(5\right)}{2\ln\left(3\right)-\ln\left(5\right)}\]