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