SOLUTION: Could you please help?! I'm trying to finish my online Algebra 2 class and the logarithm section is killing me. I cannot even begin to solve these three. Write the equation log

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Question 262571: Could you please help?! I'm trying to finish my online Algebra 2 class and the logarithm section is killing me. I cannot even begin to solve these three.
Write the equation log[base6](1/36)=-2
Evaluate the expression log[base12]12^2
Solve the equation log[base b]9=2

Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
1.) Write the equation log[base6](1/36)=-2
2.) Evaluate the expression log[base12]12^2
3.) Solve the equation log[base b]9=2
Remember the definition of a log is:
log[base a] x = b if and only if a^b = x (where a^b is a raised to the b power)
So for 1.)
log[base6] 1/36 = -2 if and only if 6^-2 = 1/36
6^-2 = 1/6^2 = 1/36
2.) log[base12] 12^2 = b if and only if 12^b = 12^2
12^b = 12^2 so b = 2
So we have log[base12] 12^2 = 2
3.) log[baseb] 9 = 2
By definition of the log we know that:
b^2 = 9
b*b = 9
b = 3
So we have log[base3] 9 = 2