Question

Use the laws of logs to combine expressions. Work right to left in laws.

Answer 1

By the power property of logarithms,

we have

$2(\log _5x+2\log _5y-3\log _5z=2\log _5x+4\log _5y^{}-6\log _5z=\log _5x^2+\log _5y^4-\log _5z^6$

Finally, by the product andf quotient property

we get

$\log _5x^2+\log _5y^4-\log _5z^6=\log _5(\frac{x^2y^4}{z^6})$

then the answer is

$\log _5(\frac{x^2y^4}{z^6})$