Question

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

Answer 1

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 $\log_x\left(x\right) = 1$ 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,

$\log_6\left(\frac{1}{36}\right)=\log_6\left(\frac{1}{6^2}\right)$

$\log_6\left(\frac{1}{36}\right)=\log_6\left(6^{-2}\right)$

$\log_6\left(\frac{1}{36}\right)=-2*\log_6\left(6\right)$ Use log rule 1 (see above)

$\log_6\left(\frac{1}{36}\right)=-2*1$ Use log rule 2 (see above)

$\log_6\left(\frac{1}{36}\right)=-2$ 

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

Answer 2

㏒₆ $\frac{1}{36}$
so 6² = 36
therefore, 6⁻² = $\frac{1}{36}$

so your answer will be -2
the power is the answer