Question 368653
{{{ln((x^4y^2)/z^(1/2))}}}
There are three properties of logarithms which can be used to manipulate them:<ul><li>{{{log(a, (p*q)) = log(a, (p)) + log(a, (q))}}}</li><li>{{{log(a, (p/q)) = log(a, (p)) - log(a, (q))}}}</li><li>{{{log(a, (p^q)) = q*log(a, (p))}}}</li></ul>
Since the argument of your logarithm is a division/fraction, we will use the second property to split it into two logarithms:
{{{ln(x^4y^2) - ln(z^(1/2))}}}
The argument of the first logarithm is a product so we will use the first property to split it into two logarithms:
{{{ln(x^4) + ln(y^2) - ln(z^(1/2))}}}
The arguments all three logarithms have an exponent. We can use the third property on them to move the argument out in front:
{{{4*ln(x) + 2*ln(y) - (1/2)*ln(z)}}}
By using the properties as we have, the expression as a whole is more complex but the arguments of the logarithms are now just a simple variable.