SOLUTION: What does it mean and how can I solve it in a equation? (log(2,x))^2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What does it mean and how can I solve it in a equation? (log(2,x))^2      Log On


   

Question 202715: What does it mean and how can I solve it in a equation?
(log(2,x))^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28log%282%2Cx%29%29%5E2+=+log%282%2Cx%29%2Alog%282%2Cx%29
To solve an equation with this expression in it we would need the equation. If it was something like:
%28log%282%2Cx%29%29%5E2+=+25 we could start by subtracting 25 from both sides giving:
%28log%282%2Cx%29%29%5E2+-+25+=+0
Then factor:
%28%28log%282%2Cx%29%29+%2B+5%29%28%28log%282%2Cx%29%29+-+5%29+=+0
In order for this (or any product) to be zero, one of the factors must be zero. So
%28log%282%2Cx%29%29+%2B+5+=+0 or %28log%282%2Cx%29%29+-+5+=+0
Solving these we subtract 5 from both sides of the first equation and add 5 to both sides of the second equation:
log%282%2Cx%29+=+-5 or log%282%2Cx%29+=+5
And then rewrite them in exponential form:
x+=+2%5E%28-5%29+=+1%2F%282%5E5%29+=+1%2F32 or x+=+2%5E5+=+32
Our solutions to this made-up problem are: x+=+1%2F32 or x+=+32