Lg(3x-2) +lg(x+1) =2 –lg2

x = 4 or x = -13/4 = -4.33

Step-by-step explanation:

log (3x - 2) + log (x + 1) = 2 - log 2

Note 2 is also equals to log 100

log (3x - 2) + log (x + 1) = log 100 - log 2

log (3x - 2)(x + 1) = log (100/2)

log 3x² + 3x - 2x - 2 = log 50

log 3x² + x - 2 = log 50

3x² + x - 2 = 50

3x² + x - 2 - 50 = 0

3x² + x - 52 = 0

find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.

3x² - 12x + 13x - 52 = 0

3x(x - 4) + 13( x - 4) = 0

(3x + 13)(x - 4) = 0

x = 4 or x = -13/4 = -4.33

If you insert 4 in the logarithm equation you will see that the left side is equal to the right

log (3x - 2) + log (x + 1) = log 100 - log 2

log 10 + log 5 = log 50

log 50 = log 50