Question 262571
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