How would you solve different logs?

What is log log_5^^5^7

1 Answer
Apr 25, 2018

7

Explanation:

  1. For this question:
    The easiest way to think about logs for most people is to think of them in terms of their exponential inverses.
    For example, log_10 100=2 because the base (10) raised to the answer (2) equals the thing you're taking the log of (100). As an equation, log_10 100=2 because 10^2=100.
    Similarly, log_2 8=3 because 2^3=8.
    Looking back at your question, let's give it an answer x.
    Then log_5 5^7=x. Putting that in exponential form, 5^7 =5^x, makes it clear that x=7.

  2. For other, non-standard base logs, use the change of base formula. Divide the log of the big number (here it's 5^7) by the log of the little number (5). So (log 5^7)/(log 5) =7. You can even use natural logs for this function! (ln 5^7)/(ln 5) =7 too.

  3. I find it handy to keep in mind the two examples I gave earlier when I'm thinking about logarithms: log_10 100=2 and log_2 8=3. Writing formulas you know at the top of your paper will help you think through new problems.

Hope this helps, and Happy mathing!