Answer:
[tex]3\log7x - 4\log7y = log(\frac{x^3}{7y^4} )[/tex]
Step-by-step explanation:
The given logarithm can be re-written as:
[tex]\log(7x)^3 - log(7y)^4[/tex]
For the power property:
[tex]\log_ba^c = c\log_ba[/tex]
Know for the quotient property you get:
[tex]log_ba - log_bc = log(\frac{a}{c} )[/tex]
[tex]\log{\frac{(7x)^3}{(7y)^4} } =\log{\frac{7^3x^3}{7^4y^4} } =\log{\frac{x^3}{7y^4} }[/tex]
so the final answer is [tex]\log{\frac{x^3}{7y^4} }[/tex]
