Question

Write 3log7x-4log7y as a single logarithm.

Answer 1

`3\log7x - 4\log7y = log((x^3)/(7y^4) )`

Explanation:

The given logarithm can be re-written as:

`\log(7x)^3 - log(7y)^4`

For the power property:

`\log_ba^c = c\log_ba`

Know for the quotient property you get:

`log_ba - log_bc = log((a)/(c) )`

`\log{((7x)^3)/((7y)^4) } =\log{(7^3x^3)/(7^4y^4) } =\log{(x^3)/(7y^4) }`

so the final answer is
`\log{(x^3)/(7y^4) }`