Question 108943
USING THE LOG PROPERTIES WRITE THE FOLLOWING AS A SINGLE LOG. EXPRESS ANY EXPONENTS AS EXPONENTS RATHER THAN FACTORS
LOG(X^5/X-5) + LOG(3(X-5)/X)-3LOGx
:
{{{log((x^5/(x-5))))}}} + {{{log((3(x-5)/x))}}} - {{{3log((x))}}}
:
Adding logs means multiply, and express as an exponent
{{{log(((x^5/(x-5))*(3(x-5)/x)))}}} - {{{log((x^3))}}}
:
Note that we can so some serious canceling inside the 1st radical, leaving us with:
{{{log((3x^4))}}} - {{{log(x^3)}}}
:
Subtracting logs means divide:
{{{log((3x^4/x^3))}}} = {{{log((3x))}}}