#1**0 **

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