SOLUTION: Solve logx + log(x-48) = 2

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Question 105757: Solve logx + log(x-48) = 2
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%29+%2B+log%28x-48%29+=+2
Read my lesson,"An overview to the laws of logarithms"

log%28x%28x-48%29%29=2
The antilogarithm of any number a, is the number who has a logarithm of a.

antilog%28log%28x%28x-48%29%29%29=antilog%282%29

Take note that log%2810%5E2%29=2. Thus, antilog%282%29=10%5E2=100
x%28x-48%29=100
x%5E2-48x=100
x%5E2-48x-100=0
By the quadratic formula,
x=%2848%2B-sqrt%2848%5E2-4%2A1%2A%28-100%29%29%29%2F%282%2A1%29
x=%2848%2B-sqrt%282304%2B400%29%29%2F%282%29
x=%2848%2B-sqrt%282704%29%29%2F%282%29
x=%2848%2B-+52%29%2F%282%29
x=-2 or x=50

Power up,
HyperBrain!