Pre calc solve with log help?

Question

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

Answer 1

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General rules:

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