Question

solve for X
log (X^2 - 4) - log (X + 2) = log 3​

Answer 1

Answer:

x = 10

Step-by-step explanation:

log (x² - 4) - log (x + 2) = log 3

Using Quotient rule : log a - log b = log a/b

log (x² - 4)/(x + 2) = log 3

(x² - 4)/(x + 2) = 3

x² - 4 = 3(x + 2)

x² - 4 = 3x + 6

x² - 3x - 4 - 6 = 0

x² - 3x - 10 = 0

x² - 5x + 2x - 10 = 0

x( x - 5 ) + 2( x - 10 ) = 0

( x + 2 )( x - 10 ) = 0

x + 2 = 0 OR x - 10 = 0

x = - 2 OR x = 10

x = - 2 is neglected since log 0 doesn't exist.

Therefore x = 10