Question

log[4](xy)^3 - log[4](xy) Simplify this

Answer 1

\[\log \left(\begin{matrix}m \\ n\end{matrix}\right) - \log \left(\begin{matrix}n \\a\end{matrix}\right) = \log \left(\begin{matrix}m \div n \\ a\end{matrix}\right)\]

Answer 2

can u give the equation using equation editor...

Answer 3

\[\LARGE \log_{4}(xy)^3-\log_{4}(xy)=\log_{4}\left(\frac{x^3y^3}{xy}\right)\]

Answer 4

continue...

Answer 5

\[\log((xy)^4)-\log(xy)=\log(\frac{x^4y^4}{xy})=\log(x^3y^3)=\log((xy)^3)=3\log(xy)\] is one method

Answer 6

simpler method is
\[\log((xy)^4)-\log(xy)=4\log(xy)-\log(xy)=3\log(xy)\]

Answer 7

silly me it is
\[\log((xy)^3)\]so answer is
\[2\log(xy)\]

Answer 8

log[4](xy)^3 - log[4](xy)
=3log[4]x + 3log[4]y - (log[4]x + log[4] y)
=2log[4]x + 2log[4]y
=2log[4](xy)
=log[4](xy)^2
is this correct?