1) lg a + lg b ≡ lg ab, so lg (1-x) + lg(1+x) = lg (1-x)(1+x) = lg (1 - x²).

lg 1 - x² = lg 0.75

1 - x² = 0.75

x² = 0.25

x = √0.25 = 0.5

2) a lg b ≡ lg b^a, so 2 lg x = lg x²

lg x² = lg 2 + lg 18 = lg 36

x⊃ 2 = 36

x = 6

3) lg a - lg b ≡ lg (a/b), so 2 lg x - lg 4 = lg (x²/4)

lg (x²/4) = lg (3x + 16)

x²/4 = 3x + 16

x² - 12x - 64 = 0

(x+4)(x-16) = 0

x = 16, because you can't have negative logarithms.

4) log6 2 + log6 3 = log6 6 = 1, because 6^1 = 6