SOLUTION: log2(5-x)+log2(5+x)=4

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Question 286068: log2(5-x)+log2(5+x)=4
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%5B2%5D%285-x%29%2BLog%5B2%5D%285%2Bx%29+=+4 Apply the "product rule" for logarithms: highlight_green%28Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29+=+Log%5Bb%5D%28M%2AN%29%29
Log%5B2%5D%28%285-x%29%285%2Bx%29%29+=+4 Simplify the left side.
Log%5B2%5D%2825-x%5E2%29+=+4 Recall the definition of the logarithm:
"The logarithm of a number (or an expression) is the power to which the base must be raised to equal that number (or expression)"
Rewrite the above equation accordingly:
2%5E4+=+25-x%5E2 Simplify.
16+=+25-x%5E2 Rearrange into a standard quadratic equation.
x%5E2-9+=+0 Factor the left side.
%28x%2B3%29%28x-3%29+=+0 Apply the "zero product rule"
x%2B3+=+0 or x-3+=+0 therefore:
x+=+-3 or x+=+3