Question

3^(x-2) = 5^(x+1)

Answer 1

Answer:

$x=log_{\frac{3}{5} }(45)$

$x-2=log_{3}(5)x+log_{3}(5) \\x-log_{3}(5)x=log_{3}(5)+2\\(1-log_{3}(5))x=log_{3}(5)+2\\x=\frac{log_{3}(5)+2}{1-log_{3}(5)} \\x=\frac{log_{3}(5)+log_{3}(3^2)}{log_{3}(3)-log_{3}(5)} \\x=\frac{log_{3}(5x3^2)}{log_{3}(\frac{3}{5} )} \\x=\frac{log_{3}(5x9)}{log_{3}(\frac{3}{5} )} \\x=\frac{log_{3}(45)}{log_{3}(\frac{3}{5} )}\\x=log_{\frac{3}{5}}(45)$

Hope this helps you :)