The logarithmic expression is
[tex] log (\sqrt{z^5}/(x^3y)) [/tex]
To expand the expression we have to use some properties of logarithm.
We know that [tex] log(m/n) = log (m) - log(n) [/tex]
By using this property we can write,
[tex] log(\sqrt{z^5}) - log(x^3y) [/tex]
Square root means to the power 1/2, so for [tex] \sqrt{z^5} [/tex], we can write [tex] z^(5/2) [/tex].
[tex] log(z^(5/2)) - log(x^3y) [/tex]
Now we have to use another property of logarithm.
We know that, [tex] log(mn) = log(m) + log(n) [/tex]
So we will use this property to [tex] log(x^3y) [/tex]
[tex] log(z^(5/2)) - log(x^3y) [/tex]
[tex] log(z^(5/2)) - (log(x^3) + log(y)) [/tex]
[tex] log(z^(5/2)) - log(x^3) - log(y) [/tex]
Now we have to use another property of logarithm.
We know that, [tex] log(a^m) = m log(a) [/tex]
By using this property we can write,
[tex] (5/2)log(z) - 3log(x) - log(y) [/tex]
This is the required aswer here.
we have logarthmic division function .
[tex] log(\frac{\sqrt{z^5}}{x^3y} ) [/tex]
we know that [tex] log(a/b)=log a-log b [/tex]
so the given function will be [tex] log(\sqrt{z^5} )-log(x^3y)=\frac{5}{2} logz-(3logx+logy) [/tex]
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 .
