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# 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# . 
For other, nonstandard 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# 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!