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14 April, 11:19

Solve log (x^2-6) = 1+log (x-3).

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  1. 14 April, 13:02
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    Log (x²-6) = 1+log (x-3)

    log (x²-6) = log 10 + log (x-3) (log 10=1)

    log (x²-6) = log (10 (x-3)) (log a+log b=log (a*b))

    Then:

    x²-6=10 (x-3)

    x²-6=10x-30

    x²-10x+24=0

    x=[10⁺₋√ (100-96) ]/2

    = (10⁺₋2) / 2

    We have two possible solutions:

    x₁ = (10-2) / 2=4

    We can check it out this solution:

    log (4²-6) = log (16-6) = log 10=1

    1+log (x-3) = 1+log (4-3) = 1 + log 1=1+0=1

    This solution is rigth.

    x₂ = (10+2) / 2=6

    We can check it out this possible solution:

    log (6²-6) = log (36-6) = log 30≈1.477121255

    1+log (x-3) = 1+log (6-3) = 1 + log 3=1.477121255

    This solution is right too.

    Answer: we have two solutions; x₁=4 and x₂=6.
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