Question

How do I tell if I need to solve using ln or log?
24^(3x)=6^(2x+1)

Answer 1

Both will yield the same end result but sometimes a particular log may be more suitable in a given situation. If "e" is not involved I'd choose log. Sometimes a different base other than base 10 or base e may be more appropriate.

Answer 2

Thank you!

Answer 3

\[ \Large
24^{3x} = 6^{2x+1} \\
\\ \text{ } \\
\text{Take log on both sides:} \\
\\ \text{ } \\
\Large \log(24^{3x}) = \log(6^{2x+1}) \\
\Large 3x\log(24) = (2x+1)\log(6) \\
\Large 3x\log(24) = 2x\log(6)+\log(6) \\
\Large 3x\log(24) - 2x\log(6) = \log(6) \\
\Large x\{3\log(24) - 2\log(6)\} = \log(6) \\
\\ \text{ } \\
\Large x = \frac{\log(6)}{3\log(24) - 2\log(6)} ~~\text{or} \\
\text{ } \\
\Large x = \frac{\ln(6)}{3\ln(24) - 2\ln(6)}
\]
You can use a calculator to compute x by both methods and you will get the same answer.