Solve 3^x=15 by taking the natural logarithm of both sides.

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- IsTim

Solve 3^x=15 by taking the natural logarithm of both sides.

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- anonymous

x log3 = log15
x = log15/log3

- roadjester

The natural logarithm is ln not log

- roadjester

\[3^x = 15\]
\[\ln 3^{3^x} =\ln 3^{15}\]
\[x=15\ln3\]

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## More answers

- roadjester

Is that the answer you have?

- IsTim

I just didn't know what to to do. Thanks though, Roadjester.

- roadjester

Do you know the Laws of Logs?

- roadjester

They are the same for natural log, just that you use natural log for the change of base formula.

- IsTim

What's the difference between natural and common logarithms? I think people may have applied the incorrect technique into my other question.

- roadjester

Well, this is the general form for log: \[\log_{a}x \] where x is a variable and a is the base. This is basically the inverse of an exponential function of the form:\[x = a^y\].
You'll notice that rather than writing the usual "y is a function of x" I have it reversed. If you're familiar with inverse functions, this shouldn't be too troublesome.

- roadjester

Now as for what the difference between \[\ln x\] and \[\log_{} x\] is, you'll notice that when I wrote log x, I had a base a. log can take on any base. The natural log is assumed to have the base of e which is approximately 2.7182818...

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