Respuesta :
ANSWER:
[tex]\log _3(\frac{25\cdot(x-7)^{\frac{2}{3}}}{(x+2)^2})[/tex]STEP-BY-STEP EXPLANATION:
We have the following logarithm:
[tex]2\log _3\mleft(5\mright)-\frac{1}{2}\log _3\mleft(x+2\mright)^4+2\log _3\mleft(\sqrt[6]{x-7}\mright)^2[/tex]Applying the properties we can combine so that it is in a single logarithm, just like this:
[tex]\begin{gathered} 2\log _3(5)=\log _3(5^2)=\log _3(25) \\ \frac{1}{2}\log _3(x+2)^4=\log _3((x+2)^{4^{}})^{\frac{1}{2}}=\log _3(x+2)^2 \\ 2\log _3(\sqrt[6]{x-7})^2=\log _3((\sqrt[6]{x-7})^2)^2=\log _3(\sqrt[6]{x-7})^4=\log _3(x-7)^{\frac{2}{3}} \\ \log _3(25^{})-\log _3(x+2)^2+\log _3(x-7)^{\frac{2}{3}}=\log _3(\frac{25\cdot(x-7)^{\frac{2}{3}}}{(x+2)^2}) \end{gathered}[/tex]