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

1 Answer

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  • DWRead
    Lv 7
    7 years ago
    Favorite Answer

    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

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