IsTim
  • IsTim
Solve 3^x=15 by taking the natural logarithm of both sides.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
x log3 = log15 x = log15/log3
roadjester
  • roadjester
The natural logarithm is ln not log
roadjester
  • roadjester
\[3^x = 15\] \[\ln 3^{3^x} =\ln 3^{15}\] \[x=15\ln3\]

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roadjester
  • roadjester
Is that the answer you have?
IsTim
  • IsTim
I just didn't know what to to do. Thanks though, Roadjester.
roadjester
  • roadjester
Do you know the Laws of Logs?
roadjester
  • roadjester
They are the same for natural log, just that you use natural log for the change of base formula.
IsTim
  • IsTim
What's the difference between natural and common logarithms? I think people may have applied the incorrect technique into my other question.
roadjester
  • 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
  • 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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