Question

Expand a logarithmic expression

Answer 1

we have logarthmic division function .

`log((√(z^5))/(x^3y) )`

we know that
`log(a/b)=log a-log b`

so the given function will be
`log(√(z^5) )-log(x^3y)=(5)/(2) logz-(3logx+logy)`

we know that if a exponent in log is bought down it will be multiplied with log

so we got square root of z^5 and x^3 as 5/2 and 3 .

Answer 2

The logarithmic expression is

`log (√(z^5)/(x^3y))`

To expand the expression we have to use some properties of logarithm.

We know that
`log(m/n) = log (m) - log(n)`

By using this property we can write,

`log(√(z^5)) - log(x^3y)`

Square root means to the power 1/2, so for
`√(z^5)`, we can write
`z^(5/2)`.

`log(z^(5/2)) - log(x^3y)`

Now we have to use another property of logarithm.

We know that,
`log(mn) = log(m) + log(n)`

So we will use this property to
`log(x^3y)`

`log(z^(5/2)) - log(x^3y)`

`log(z^(5/2)) - (log(x^3) + log(y))`

`log(z^(5/2)) - log(x^3) - log(y)`

Now we have to use another property of logarithm.

We know that,
`log(a^m) = m log(a)`

By using this property we can write,

`(5/2)log(z) - 3log(x) - log(y)`

This is the required aswer here.