Question 354490
{{{log(2, ((sqrt(x)(x-5))/y^3))}}}
We can start by using a property of logarithms, {{{log(a, (p/q)) = log(a, (p)) - log(a, (q))}}}, to split the log of a fraction into separate logs:
{{{log(2, (sqrt(x)(x-5))) - log(2, (y^3))}}}
Next, on the first log, we can use another property of logarithms, {{{log(a, (p*q)) = log(a, (p)) + log(a, (q))}}}, to separate the log of a product into separate logs:
{{{log(2, (sqrt(x))) + log(2, (x-5)) - log(2, (y^3))}}}
This is as many logs as we can get. But often these problems want you to use yet a third property of logarithms, {{{log(a, (p^q)) = q*log(a, (p))}}}, to remove exponents. But first, we will rewrite the square root using a fractional exponent:
{{{log(2, (x^(1/2))) + log(2, (x-5)) - log(2, (y^3))}}}
Now we will use the property on the first and last logs to move their exponents out in front:
{{{(1/2)log(2, (x)) + log(2, (x-5)) - 3*log(2, (y))}}}