SOLUTION: Please help me write this expression as a single logarithm: -2log(1/x)+(1/3)log(sqrt(x)) the base of each log is 3 I know that first you have to switch the coefficients an

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me write this expression as a single logarithm: -2log(1/x)+(1/3)log(sqrt(x)) the base of each log is 3 I know that first you have to switch the coefficients an      Log On


   



Question 734032: Please help me write this expression as a single logarithm:
-2log(1/x)+(1/3)log(sqrt(x))
the base of each log is 3
I know that first you have to switch the coefficients and make them exponents, and when your exponent is 1/3 it is really the cube root, in this case, of sqrt(x). But how do you go from there? How can you cube root a square root? And when you put the 2 to be an exponent does the negative sign go with it or does it stay part of the log? Please help me, I am so confused.

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28x%29%29%5E2 = sqrt%28x%29%2Asqrt%28x%29=x

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x%5E%281%2F2%29%2Ax%5E%281%2F2%29 = x%5E%281%2F2%2B1%2F2%29=x%5E1=x

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%28sqrt%28x%29%29%5E%281%2F3%29=%28x%5E%281%2F2%29%29%5E%281%2F3%29
%28x%5E%281%2F2%29%29%5E%281%2F3%29=x%5E%28%281%2F2%29%281%2F3%29%29
=x%5E%281%2F6%29