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

1. LordHades Group Title

x log3 = log15 x = log15/log3

2. roadjester Group Title

The natural logarithm is ln not log

3. roadjester Group Title

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

4. roadjester Group Title

Is that the answer you have?

5. IsTim Group Title

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

6. roadjester Group Title

Do you know the Laws of Logs?

7. roadjester Group Title

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

8. IsTim Group Title

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

9. roadjester Group Title

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 Group Title

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...