slove the equation logx24 logx2 2 logx2Solutionlogx24 log

slove the equation. log(x²+4) - log(x+2) = 2+ log(x-2)

Solution

log(x2+4) - log(x+2) = 2+ log(x-2)

use the log property: loga -logb = log(a/b and loga +logb = log(a*b)

log(x^2+4)/(x+2) = 2+log(x-2)

log(x^2+4)/(x+2) - log(x-2) = 2

log(x^2+4)/(x^2 -4) = 2

(x^2 +4)/(x^2 -4) = 10^2

(x^2 +4) = 100(x^2 -4)

x^2 +4 = 100x^2 -400

-99x^2 = -404

x^2 = 404/99

x = sqrt(404/99) = 2.02

x= 2.02