Question

1) log sub 8 2 + log sub 8 4x^2 = 1

2) ln 2 - ln (3x + 2) = 1
3) ln (x - 3) - ln (x - 5) = ln 5

Answer 1

log_8(2)+log_8(4x^2) = 1

1/3 + log_8(4) + log_8(x^2) = 1
1/3 + 2/3 + log_8(x^2) = 1
log_8(x^2) = 0
x^2 = 1
x = ±1

ln2 - ln(3x+2) = 1
ln (2/(3x+2)) = 1
2/(3x+2) = e
2/e = 3x+2
x = (2/e - 2)/3 = 2(1-e) / 3e

ln(x-3) - ln(x-5) = ln 5
(x-3)/(x-5) = 5
x-3 = 5x-25
x = 11/2