Question 33712
First, note that when factoring a binomial in the form: {{{a^3 - b^3}}}, it is simplified as {{{(a - b)*(a^2+ab+b^2)}}}. <font size = "-2">You can use the distributive property to verify this.</font>
Also, note that the quotient property of logarithms states: {{{log(a)-log(b) = log (a/b)}}}.

First, replace {{{x^3 - 8}}} with {{{x^3 - 2^3}}}.
Use the first property I explained. This will simplify to
{{{log((x-2)(x^2+2x+4)) - log (x-2)}}}.
Use the second property.
{{{log(((x-2)(x^2+2x+4))/(x-2))}}}.
Simplify by canceling the {{{x-2}}} and you are left with the answer:
{{{log(x^2+2x+4)}}}
<marquee behavior="alternate"> NtNk</marquee>