By the power property of logarithms,
we have
[tex]2(\log _5x+2\log _5y-3\log _5z=2\log _5x+4\log _5y^{}-6\log _5z=\log _5x^2+\log _5y^4-\log _5z^6[/tex]
Finally, by the product andf quotient property
we get
[tex]\log _5x^2+\log _5y^4-\log _5z^6=\log _5(\frac{x^2y^4}{z^6})[/tex]
then the answer is
[tex]\log _5(\frac{x^2y^4}{z^6})[/tex]
