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How do I solve

log(10x+5)-log(4-x)=100

Guest Feb 21, 2017
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Solve for x:
log(10 x + 5) - log(4 - x) = 100

log(10 x + 5) - log(4 - x) = log(1/(4 - x)) + log(10 x + 5) = log((10 x + 5)/(4 - x)):
log((10 x + 5)/(4 - x)) = 100

Cancel logarithms by taking exp of both sides:
(10 x + 5)/(4 - x) = e^100

Multiply both sides by 4 - x:
10 x + 5 = e^100 (4 - x)

Expand out terms of the right hand side:
10 x + 5 = 4 e^100 - e^100 x

Subtract 5 - e^100 x from both sides:
(e^100 + 10) x = 4 e^100 - 5

Divide both sides by e^100 + 10:
Answer: |x = (4 e^100 - 5)/(e^100 + 10) = 4

Guest Feb 21, 2017

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