SOLUTION: simplify this expression: logx + logx^(3/2) - -2logx i'm fairly sure you end up with {{{ log(sqrt( x ) / x) }}} but i'm not 100% certain, if someone could confirm & maybe even

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: simplify this expression: logx + logx^(3/2) - -2logx i'm fairly sure you end up with {{{ log(sqrt( x ) / x) }}} but i'm not 100% certain, if someone could confirm & maybe even      Log On


   



Question 1061613: simplify this expression:
logx + logx^(3/2) - -2logx
i'm fairly sure you end up with +log%28sqrt%28+x+%29+%2F+x%29+ but i'm not 100% certain, if someone could confirm & maybe even show steps that would be awesome! thank you!

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
logx + logx^(3/2) - -2logx

Notice that you have two - signs in a row.  Was that a typo, and
there should have been only 1 - sign? 
I'll assume so, that you mean this:

log%28%28x%29%29%2Blog%28%28x%5E%283%2F2%29%29%29-2%2Alog%28%28x%29%29

The first and last terms are like terms, so 
combine them:  1*log(x)-2*log(x) gives -1*log(x)

-1%2Alog%28%28x%29%29%2Blog%28%28x%5E%283%2F2%29%29%29


Move the -1 coefficient of the first term to the
exponent of what the log is of, which is x, making
the x become x-1

log%28%28x%5E%28-1%29%29%29%2Blog%28%28x%5E%283%2F2%29%29%29

Write the sum of those two logs as the log of a
product: 

log%28%28x%5E%28-1%29%2Ax%5E%283%2F2%29%29%29

Simplify by adding the exponents of x:

log%28%28x%5E%28-1%2B3%2F2%29%29%29

log%28%28x%5E%28-2%2F2%2B3%2F2%29%29%29

log%28%28x%5E%281%2F2%29%29%29

log%28%28sqrt%28x%29%5E%22%22+%29%29

Edwin