Solving an exponential equation using natural logs

[jaguar]

I am trying to help my son with the following problem and cannot remember how to solve it when the bases are different. He doesn't have his book here for me to review.

6^(3x-5) = 2^(7x)

Any steps/hints you can provide would be appreciated since I haven't touched this stuff in 30 years.

Thank you!

 

[pka]

\(\displaystyle \begin{array}{rcl}
6^{\left( {3x - 5} \right)} & = & 2^{\left( {7x} \right)} \\
\left( {3x - 5} \right)\ln (6) & = & \left( {7x} \right)\ln (2) \\
\end{array}.\)

Now solve for x.

 

[stapel]

He doesn't have his book here for me to review.... Any steps/hints you can provide would be appreciated since I haven't touched this stuff in 30 years.

Since we cannot teach the requested material within this environment, please review some of the lessons available online:

. . . . .Google results for "solve exponential equation"

If you need some of the background material (such as logs, log rules, solving log equations, etc), please specify, and we can try to find some links for those topics as well.

Once you have learned the background materials, please attempt the exercise. If you get stuck, please reply showing all of your work and reasoning. Thank you.

Eliz.