How would you solve different logs?
What is log log_5^^5^7
What is log
1 Answer
7
Explanation:
-
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 because10^2=100 .
Similarly,log_2 8=3 because2^3=8 .
Looking back at your question, let's give it an answerx .
Thenlog_5 5^7=x . Putting that in exponential form,5^7 =5^x , makes it clear thatx=7 . -
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. -
I find it handy to keep in mind the two examples I gave earlier when I'm thinking about logarithms:
log_10 100=2 andlog_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!