First off, I am so happy we are on logs! I LOVE logs! The number one thing you should know when solving a log is the basic formula (exponential form) which happens to be b^a=x while log for would be log b^x=a. When a problem does not have anything on the opposite side of the equal sign (opposite of log), put an x. If a log problem doesn't have a base, it is understood to be 10 because 10 is the default base.
Examples:
log3^9=2
In order to solve, you need to put this into exponential form...
3^2=9
...and that is your answer.
log2^16=4
2^4=16
log5^125=x
5^x=125 (if it asks for exponential form)
x=3 (if it says to solve)
log x=2
10^2=x
x=100
logx^8=3
x^3=8
x=2
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