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## IsTim 2 years ago Solve 3^x=15 by taking the natural logarithm of both sides.

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1. LordHades

x log3 = log15 x = log15/log3

2. roadjester

The natural logarithm is ln not log

3. roadjester

$3^x = 15$ $\ln 3^{3^x} =\ln 3^{15}$ $x=15\ln3$

4. roadjester

Is that the answer you have?

5. IsTim

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

6. roadjester

Do you know the Laws of Logs?

7. roadjester

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

8. IsTim

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

9. 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.

10. 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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