SOLUTION: Can someone please explain how to solve the following problem. Your assistance is greatly appreciated! Express in terms of sums and differences of logarithms log square root of x

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Can someone please explain how to solve the following problem. Your assistance is greatly appreciated! Express in terms of sums and differences of logarithms log square root of x      Log On


   

Question 170275: Can someone please explain how to solve the following problem. Your assistance is greatly appreciated!
Express in terms of sums and differences of logarithms
log square root of x^4/yz
Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
log square root of x^4/yz
= log(sqrt(x^4/yz))
= log(x^2*sqrt(1/yz))
= 2*log(x) + 1/2log(1/yz)
= 2*log(x) - 1/2log(yz)
= 2log(x) - 1/2(log(y) -1/2log(z)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Express in terms of sums or differences:
Log%28sqrt%28x%5E4%2Fyz%29%29 Rewrite the square root as an exponent:
Log%28x%5E4%2Fyz%29%5E%281%2F2%29 Apply the "power" rule.
%281%2F2%29Log%28x%5E4%2Fyz%29 Now apply the "quotient" rule.
%281%2F2%29%28Log%28x%5E4%29-Log%28yz%29%29 You can apply the "power" rule again to the first log.
%281%2F2%29%284Log%28x%29-Log%28yz%29%29 Now apply the "product" rule to the second logarithm.
%281%2F2%29%284Log%28x%29-%28Log%28y%29%2BLog%28z%29%29%29 Finally, multiply through by 1/2 to simplify.
2Log%28x%29-%281%2F2%29Log%28y%29-%281%2F2%29Log%28z%29 and this can also be written as:
Log%28x%5E2%29-Log%28sqrt%28y%29%29-Log%28sqrt%28z%29%29