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

Question

anonymous · Answer

x log3 = log15
x = log15/log3

roadjester · Answer

The natural logarithm is ln not log

roadjester · Answer

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

roadjester · Answer

Is that the answer you have?

istim · Answer

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

roadjester · Answer

Do you know the Laws of Logs?

roadjester · Answer

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

istim · Answer

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

roadjester · Answer

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 · Answer

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...