Question

properties of logarithms: 3^x=5^x+2

Answer 1

\[3^x=5^{x+2}?\]

Answer 2

Yes

Answer 3

\[\ln(3^x)=\ln(5^{x+2})\]
\[x \ln 3=(x+2)\ln 5\]
\[x \ln 3=x \ln5+2\ln5\]
\[x(\ln3-\ln5)=2\ln5\]\[x=\frac{\ln5}{\ln3-\ln5}\]