Question 376797
{{{log(b, (x^3y^2/z))}}}
There are three properties of logarithms which can be used to manipulate arguments of logarithms:<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 your argument is a fraction/division, we willstart by using the second property to split the numerator and denominator into their own logarithms:
{{{log(b, (x^3y^2)) - log(b, (z))}}}
Next we can use the first property on the first logarithm, since its argument is a product:
{{{log(b, (x^3)) + log(b, (y^2)) - log(b, (z))}}}
And last we can use the third property on the first two logarithms, since their arguments have exponents:
{{{3*log(b, (x)) + 2*log(b, (y)) - log(b, (z))}}}
This expression is equivalent to the original expression and it it expressed in terms of the base b logarithms of x, y and z.