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Question
Hello, thank you for taking my question. It is:

Assuming that x, y and a are positive numbers, use the properties of logarithms to write the following expression in terms of logarithms of x and y. The expression is:

log(a) 9th-sqrt(xy)

Hi Leo,
I hope you mean the logarithm (to base a) of the 9th root of xy (as opposed to the "9th square root").
So, the expression would become
log(a) (xy)^(1/9)
= log(a) [x^(1/9)].[y^(1/9)]
= log(a) [x^(1/9)] + log(a) [y^(1/9)]       (since log AB = log A + log B)
= [log(a) x]/9 + [log(a) y]/9
or just
(1/9)[log(a) x + log(a) y]

Regards

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