log_5 (x-1) + log_5 (x-2) - log_5 (x+6) = 0log5(x−1)+log5(x−2)−log5(x+6)=0
color(blue)(log a + log b = log (ab), log x - log y = log(x/y), " as per log rules"loga+logb=log(ab),logx−logy=log(xy), as per log rules
log_5 (((x+1)(x-2)) / (x+6)) = 0log5((x+1)(x−2)x+6)=0
((x+1)(x-2)) / (x+6) = 5^0 = 1(x+1)(x−2)x+6=50=1
(x+1) (x-2) = x + 6(x+1)(x−2)=x+6
x^2 -x - 2 = x + 6x2−x−2=x+6
color(crimson)(x^2 = 8 " or " x = +- 2 sqrt2x2=8 or x=±2√2