Question

log (x + 2)+ log(x -2)= log 3 + 3 log 4

Answer 1

Given

log(x+2)+log (x-2) = log3+3log4

or, log (x+2)(x-2) = log3+log4^3
or,log (x^2-4) = log (3×64)
or, x^2-4 = 192
or, x^2 = 196
$or \: \: x = \sqrt{196}$
or x =14 is right answer.

Answer 2

$log(x + 2) + log(x - 2) = log(3) + 3 log(4) \\ \\ log(x + 2) + log(x - 2) = log(3) + log( {4}^{3} ) \\ \\ log(x + 2) + log(x - 2) = log(3) + log(64)$

$log[ (x + 2) \times (x - 2)] = log(3 \times 64) \\ \\ log( {x}^{2} - {2}^{2} ) = log(192) \\ \\ {x}^{2} - 4 = 192$

${x}^{2} = 192 + 4 = 196 \\ \\ x =\pm \sqrt{196} \\ \\ x = \pm \: 14 \\ \\ \text{log of negative numbers is not defined} \\ \\ so \: \boxed{x = 14}$