SOLUTION: if log(x)=16 then log(square root x)=?

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: if log(x)=16 then log(square root x)=?      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 205974: if log(x)=16 then log(square root x)=?
Found 2 solutions by RAY100, Earlsdon:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
log(x) = 16,,,raising to power of 10,,x= 1*10^16
.
sqrt x = sqrt(1*10^16) = 1 *10^8
.
log (sqrt(x)) = log(1*10^8) = 8
.
This makes sense when we review, log a^b = b * log a
.
log(sqrt(x)) = log {x}^(1/2) = (1/2) * log x,,,= (1/2) *16 = 8
.

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%29%29+=+16
log%28%28sqrt%28x%29%29%29+=+log%28%28x%29%29%5E%281%2F2%29...and...
log%28%28x%29%29%5E%281%2F2%29+=+%281%2F2%29log%28%28x%29%29 by the power rule, so...
%281%2F2%29log%28%28x%29%29+=+%281%2F2%29%2816%29
%281%2F2%29log%28%28x%29%29+=+8 so...
highlight%28log%28%28sqrt%28x%29%29%29+=+8%29