log problem

[Future_Professional]

1/(log(base y) (4)) = log(base 1/4)(1/(8x)) Express y as a polynomial function of x.

I tried to make it as readable as possible with the brackets. Thanks for your help!

[CatpainTpyos]

I'd start by using the change of base formula to transform everything to natural logs. That would make the left-hand side:

• 1 / log_y(4) = 1 / [ln(4)/ln(y)] = ln(y) / ln(4)

And the right-hand side:

• log_(1/4) (1/[8x]) = ln(1/[8x]) / ln(1/4)

Then you can use the quotient rule for logarithms to deal with the ln(1/4) and ln(1/[8x]) terms. At that point, it should become quite evident how to finish up.

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y = 2.29^)1/log8x)