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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
up vote 4 down vote accepted

This appears to be simple cancellation, and doesn't require any actual use of the logarithms or the particular base. Notice $$ \frac{(3\log_y 5)(2\log_y 5)}{(6\log_y 5)}=\frac{3\cdot 2\cdot(\log_y 5)^2}{6\log_y 5}=\log_y 5. $$

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answer will be accept and can i ask how you type the base sign and over sign? I can;t type it – dramasea May 2 '11 at 6:30
@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

By simple arithmetic,

$\frac{3 log_y(5) \cdot 2 log_y(5)}{6 log_y(5)} = \frac{6 log^2_y(5)}{6 log_y(5)} = log_y(5)$

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