SOLUTION: I need to simplify (2log2x)/2 where log2 is log base 2. An answer sheet from my teacher shows this simplifying to log2x^2 but I think this (specifically the "squared" part) is wro

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I need to simplify (2log2x)/2 where log2 is log base 2. An answer sheet from my teacher shows this simplifying to log2x^2 but I think this (specifically the "squared" part) is wro      Log On


   

Question 953289: I need to simplify (2log2x)/2 where log2 is log base 2. An answer sheet from my teacher shows this simplifying to log2x^2 but I think this (specifically the "squared" part) is wrong. Is the teacher wrong or am I missing something here? Thanks!
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You described (2*log(2,x))/2 rendered to %282%2Alog%282%2Cx%29%29%2F2

%282%2F2%29%28log%282%2Cx%29%29
1%2Alog%282%2Cx%29
log%282%2Cx%29----simplified.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Log Rules:
1) log%28b%2C%28mn%29%29+=+log%28b%2C%28m%29%29+%2B+log%28b%2C%28n%29%29
2) log%28b%2C%28m%2Fn%29%29+=+log%28b%2C%28m%29%29+%96+log%28b%2C%28n%29%29
3) log%28b%2C%28m%5En%29%29+=+highlight%28n+%2Alog%28b%2C%28m%29%29%29...you need to apply this rule



%282log%282%2Cx%29%29%2F2
%28cross%282%29log%282%2Cx%29%29%2Fcross%282%29
highlight%28log%282%2Cx%29%29..simplified using base 2
now you can change the base if you will:
In order to evaluate a non-standard-base log, you have to use the Change-of-Base formula:
log%28b%2C%28x%29%29=log%28d%2C%28x%29%29%2Flog%28d%2C%28b%29%29
usually we use base d=10
so, you will have
log%28x%29%2Flog%282%29

your teacher shows this simplifying to log%282%2Cx%5E2%29 which is wrong
2log%282%2Cx%29 is equal log%282%2Cx%5E2%29 (using the rule from above, but given
is 2log%282%2Cx%29%2F2=>is equal to log%282%2Cx%5E2%29%2F2 not only log%282%2Cx%5E2%29