Can someone answer and explain to me how to solve this? log (lowercase 6) 1/36

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 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,





Use log rule 1 (see above)

Use log rule 2 (see above)

 

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