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5 June, 18:56

What is the solution of log2x + 6 144 = 2?

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  1. 5 June, 20:19
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    2x+6 is the base

    Then the equation is logarithm of 144 on basis 2x + 6 = 2

    Then [2x + 6]^2 = 144

    Now expand the square binomial

    4x^2 + 24x + 36 = 144

    4x^2 + 24x + 36 - 144 = 0

    4x^2 + 24x - 108 = 0

    Divide by 4

    x^2 + 6x - 27 = 0

    Factor: (x + 9) (x - 3) = 0

    x = - 9 and x = 3

    The only valid is x = 3, because x = - 9 yields 2x + 6 = - 12 and the logarithm function cannot have negative basis.

    Then the answer is x = 3.
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