Question

Solve the equation 5^(x-1)=3^x round answer to 3 decimal places

Answer 1

take log both sides
\[\ln 5^{x-1} = \ln 3^{x}\]
\[(x-1) \ln 5 = x \ln 3\]
\[x \ln 5 - \ln 5 = x \ln 3\]
\[x \ln 5 - x \ln 3 = \ln 5\]
\[x = \frac{\ln 5}{\ln 5 - \ln 3}\]

Answer 2

i got 3.151

Answer 3

yep