Question

What’s the answer to this question that I am doing

Answer 1

Answer: -2 (choice B)

Work Shown:

`\log_(6)\left((1)/(36)\right) = \log_(6)\left((1)/(6^2)\right)\\\\\log_(6)\left((1)/(36)\right) = \log_(6)\left(6^(-2)\right)\\\\\log_(6)\left((1)/(36)\right) = -2*\log_(6)\left(6\right)\\\\\log_(6)\left((1)/(36)\right) = -2*1\\\\\log_(6)\left((1)/(36)\right) = -2\\\\`

Another approach is to use the change of base rule to have these steps

`\log_(b)\left(x\right) = (\log(x))/(\log(b))\\\\\log_(6)\left((1)/(36)\right) = (\log(1/36))/(\log(6))\\\\\log_(6)\left((1)/(36)\right) = (\log(6^(-2)))/(\log(6))\\\\\log_(6)\left((1)/(36)\right) = (-2*\log(6))/(\log(6))\\\\\log_(6)\left((1)/(36)\right) = -2\\\\`

I also used the log rule that log(x^y) = y*log(x).