Pre calc solve with log help?
How do you answer these questions?
Solve the following equation:
1) log2 (7x+6) = log2 (3x+2) +log2 (x+2)
2) log2 (log3 x) = 2
- DWReadLv 77 years agoFavorite Answer
log(ab) = log(a) + log(b)
If logₓ(b) = a then b = xª.
log₂(7x+6) = log₂(3x+2) + log₂(x+2)
log₂(7x+6) = log₂((3x+2)(x+2)) = log₂(3x² + 8x + 4
7x+6 = 3x² + 8x + 4
3x² + x - 2 = 0
(3x - 2)(x + 1) = 0
x = 2/3, -1, however the argument of a logarithm must be positive, so discard the negative root.
x = 2/3
log₂(log₃(x)) = 2
log₃(x) = 2² = 4
x = 3⁴ = 81