solve for x

Question

log(1-x)+log(4-x)=1

Answer 1

log (1 - x) + log (4 - x) = 1

log [(1 - x)(4 - x)] = 1             product rule

10¹ = (1 - x)(4 - x)                  definition

10 = 4 - 5x + x²

0 = x² - 5x - 6

0 = (x + 1)(x - 6)

{-1, 6}

 

6 is extraneous