Answer:
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