Question 445329
log12 (1/144) 
I know that because it is 1/144 the answer will be negative but I'm not really sure about anything else. If you could explain to me how logs work that'd be great! Thank you.
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One definition of a logarithm I find most useful is this:
The base raised to the logarithm of a number=number. This is called the exponential form of a logarithm.
In your case, the base=12, the number is 1/144 and you are trying to find the logarithm of 1/144.
In other words, what do you raise 12, to equal 1/144. 

12^x=1/144
1/144=1/12^2=12^-2
12^x=12^-2
since the bases are equal, the exponents must be equal to each other, that is,
x=-2, the logarithm of 1/144, base 12.
To check: raise 12 to -2=12^-2=1/12^2=1/144