Can I ask how to solve this?
$(3\log_y 5)(2\log_y 5) / (6\log_y 5)$
the answer is $\log_y 5$.
Can I ask how to solve this?
$(3\log_y 5)(2\log_y 5) / (6\log_y 5)$
the answer is $\log_y 5$.
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. $
By simple arithmetic,
$\frac{3 log_y(5) \cdot 2 log_y(5)}{6 log_y(5)} = \frac{6 log^2_y(5)}{6 log_y(5)} = log_y(5)$