Question

How do you expand `log ((3x(5y))/(3z^2))`?

Answer 1

`log(5)+log(x)+log(y)-2log(z)`

Explanation:

Use the following logarithm rules.

`log(AB) = log(A) + log(B)` Product Rule

`log(A/B) = logA - log(B)` Quotient Rule

`log(A^n) = nlog(A)` Power Rule

Our problem `log((3x(5y))/(3z^2))`
We can cancel out 3 from numerator and denominator.
`log((x(5y))/(z^2))`
Then apply the rules which we saw

`log((x(5y)) - log(z^2)` Applying the Quotient rule.
`log(x)+log(5)+log(y) - log(z^2)` Applying the Product rule.
`log(x)+log(5)+log(y) - 2log(z)` Applying Power Rule.

Re-arranging.
`log(5)+log(x)+log(y)-2log(z)`