Question

Solve for x:
$\log (3x+2) - \log (3x-2) = \log 5$

Answer 1

concepts : $log\frac{A}{B}=logA-logB$.....(1)

$logA=logB\implies A=B$.........(2)


now, log(3x + 2) - log(3x - 2) = log5

or, log{ (3x + 2)/(3x - 2) } = log5 [ using formula (1) ]

or, (3x + 2)/(3x - 2) = 5 [ using formula (2), ]

or, (3x + 2) = 5(3x - 2)

or, 3x + 2 = 15x - 10

or, 3x - 15x = -10 - 2

or, -12x = -12

hence, x = 1