Answer: The log simplifies to -2
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Explanation:
We will use the log rule that log(x^y) = y*log(x). Call this log rule 1. This log rule basically allows us to pull the exponent down.
Another log rule that we will use is [tex]\log_x\left(x\right) = 1[/tex] where x is any positive real number but x = 1 is NOT allowed. Call this log rule 2.
Because 36 = 6^2, this means that 1/36 = 6^(-2)
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So,
[tex]\log_6\left(\frac{1}{36}\right)=\log_6\left(\frac{1}{6^2}\right)[/tex]
[tex]\log_6\left(\frac{1}{36}\right)=\log_6\left(6^{-2}\right)[/tex]
[tex]\log_6\left(\frac{1}{36}\right)=-2*\log_6\left(6\right)[/tex] Use log rule 1 (see above)
[tex]\log_6\left(\frac{1}{36}\right)=-2*1[/tex] Use log rule 2 (see above)
[tex]\log_6\left(\frac{1}{36}\right)=-2[/tex]
This means that the given expression simplifies to -2
You can use a calculator to type in "log(1/36)/log(6)" without quotes and you should get -2 as the answer
