How do I solve the problem without Logarithms

Question

log (x+8) - log (x+1)=log 6

Answer 1

loga + logb = logab is the general formula

let a=x+8, b = x+1

(x+8)(x+1) = 6

x^2 +9x + 8 = 6

x^2 +9x +2 = 0

use the quadratic formula

x = 9/2 + or - (1/2)sqr(81-4(2)) = 4.5 + or - .5sqr73

x = about -0.23 or 8.77

check the answers

log(x+8) + log(x+1) = log6 = 0.778

log(-.23+8) + log(-.23+1) = log7.74 + log.77 = .888 -.114 = .77 = log((7.73)(.77)) = log5.95 = .77

lot(8.77+8) + log(8.77+1) = log 16.77 + log9.77 = 1.22 + .99 = 2.21 = log((16.77)(9.77)) = log163.8= 2.21

slight rounding error