How do I find the approximate value of #log_5 20#?
When approximating logarithms, I find it useful more often than not to convert it to exponential form, as it just makes it that much nicer to look at.
To convert a logarithm to exponential form, simply refer to the illustration below:
If you're curious as to how this works, please read this other answer I collaborated on. It should help :)
So if you converted
Now, we can begin making estimates.
We know that
And the answer is 1.86. Close enough :)
This is only how to estimate. If you want to get exact answers for tests or quizzes, you should either use the "logBASE" function found on TI-84 calculators, or the change of base formula, for which this video will help:
Hope that helps :)