# How to solve $(3\log_y 5)(2\log_y 5) / (6\log_y 5)$?

Can I ask how to solve this?

$$(3\log_y 5)(2\log_y 5) / (6\log_y 5)$$

the answer is $\log_y 5$.

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You mean "simplify". Note that $3\times2=6$ and that you can cancel $\log_y 5$ from the numerator and denominator. –  Ｊ. Ｍ. May 2 '11 at 6:22
if this is a homework, please tag it so. –  Thomas Connor May 2 '11 at 7:11
This appears to be simple cancellation, and doesn't require any actual use of the logarithms or the particular base. Notice $$\frac{(3\log_y 5)(2\log_y 5)}{(6\log_y 5)}=\frac{3\cdot 2\cdot(\log_y 5)^2}{6\log_y 5}=\log_y 5.$$
@dramasea, this site uses LaTeX markup. To see the way to type it, just right click on the math and choose the option "show source". To get it to render, surround the code with $. For example $\log_y 5$ typesets$\log_y 5$. Also, $\frac{a}{b}$ gives$\frac{a}{b}$if you want to write fractions. – yunone May 2 '11 at 6:33 add comment By simple arithmetic,$\frac{3 log_y(5) \cdot 2 log_y(5)}{6 log_y(5)} = \frac{6 log^2_y(5)}{6 log_y(5)} = log_y(5)\$