Solve the equation

Question

log₃(x + 4) = 1 − log₃(x + 2)

Answer 1

log₃(x+4) = 1 - log₃(x+2)

Since the sum of logarithms  is the log of the product

log₃[(x+4)(x+2)] = 1

use each side as the exponent of 3

(x+4)(x+3) = 3

x² + 6x + 8 = 3

x² + 6x +5 = 0

(x+1)(x+5) = 0

x = -1 and x =-5 are the roots

You should go back and verify that each of the roots satisfies the original equation!