Question

how to solve for x ?
5^(x-2) = 3^(3x+2)

Answer 1

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

Answer 2

5^(x-2) = 3^(3x+2)
=> 5^x / 5^2 = (3^3)^x * 3^2
=> 5^x = 225 * 27^x
=> (5/27)^x = 225
=> x ln(5/27) = ln(225)
=> x = ln(225) / ln(5/27)
=> x ≈ - 3.21.

Answer 3

@hartnn

Answer 4

why ln instead of log ? @GirlByte

Answer 5

In my opinion, I think this technique is better

Answer 6

Actually it doesn't make a diff. because \[\frac{\log x}{\log y} = \frac{\left( \frac{\ln x}{\ln 10} \right)}{\left( \frac{\ln y}{\ln 10} \right)} = \frac{\left( \frac{\ln x}{\cancel{\color{red}{\ln 10}}} \right)}{\left( \frac{\ln y}{\cancel{\color{red}{\ln 10}}} \right)} = \frac{\ln x}{\ln y}\]