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30 December, 14:15

Solve: log4 (7t + 2) = 2

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  1. 30 December, 15:22
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    log3 (x - 2) + log3 (x - 4) = log3 (2x^2 + 139) - log3 (3)

    We now use the product and quotient rules of the logarithm to rewrite the equation as follows.

    log3[ (x - 2) (x - 4) ] = log3[ (2x^2 + 139) / 3 ]

    Which gives the algebraic equation

    (x - 2) (x - 4) = (2x^2 + 139) / 3

    Mutliply all terms by 3 and simplify

    3 (x - 2) (x - 4) = (2x^2 + 139)

    Solve the above quadratic equation to obtain

    x = - 5 and x = 23

    check:

    1) x = - 5 cannot be a solution to the given equation as it would make the argument of the logarithmic functions on the right negative.

    2) x = 23

    Right Side of equation:

    log3 (23 - 2) + log3 (23 - 4) = log3 (21*19) = log3 (399)

    Left Side of equation:

    log3 (2 (23) ^2 + 139) - 1 = log3 (1197) - log3 (3) = log3 (1197 / 3) = log3 (399)

    conclusion: The solution to the above equation is x = 23
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