SOLUTION: 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

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 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 On


   

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
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%28%28x%5E5%2F%28x-5%29%29%29%29 + log%28%283%28x-5%29%2Fx%29%29 - 3log%28%28x%29%29
:
Adding logs means multiply, and express as an exponent
log%28%28%28x%5E5%2F%28x-5%29%29%2A%283%28x-5%29%2Fx%29%29%29 - log%28%28x%5E3%29%29
:
Note that we can so some serious canceling inside the 1st radical, leaving us with:
log%28%283x%5E4%29%29 - log%28x%5E3%29
:
Subtracting logs means divide:
log%28%283x%5E4%2Fx%5E3%29%29 = log%28%283x%29%29