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I know that I have to use the change of base rule...but I don't know how to apply it for fractions like this. If you can show me the steps as to how to solve this log question, it'd be greatly appreciated! Thank you.

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1 Answer

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these questions are kind of pointless but this is how you would do it.

By using change of base log8 17 becomes (loge 17)/(loge 8)

And log9 17 becomes (loge 17)/(loge 9)

So [(loge 17)/(loge 8)] / [(loge 17)/(loge 9)]=[(loge 17)/(loge 8)] * [(loge 9)/(loge 17)]
the (loge 17)'s cancel so you are left with (loge 9)/(loge 8) = (loge 3^2)/(loge 2^3) = 2(loge 3)/3(loge 2)

If it asks for an answer in decimals you would then put this in your calculator
I hope you can follow the working, it's hard to express it properly here.

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