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Solve the following exponential equation
5^2-x=7^5x+7

  • Math -

    5 ^ 2 = 25

    7 ^ 5 = 16,807


    5 ^ 2 - x = 7 ^ 5 x + 7

    25 - x = 16,807 x + 7 Add x to both sides

    25 - x + x = 16,807 x + 7 + x

    25 = 16,808 x + 7 Subtract 7 to both sides

    25 - 7 = 16,808 x + 7 - 7

    18 = 16,808 x Divide both sides by 16,808

    18 / 16,808 = 16,808 x / 16,808

    18 / 16,808 = x

    2 * 9 / ( 2 * 8,404 ) = x

    9 / 8,404 = x

    x = 9 / 8,404

  • Math -

    If you mean,
    5^(2-x) = 7^(5x + 7)
    Then, we take the ln of both sides
    (2-x)*ln(5) = (5x + 7)*ln(7)
    1.609*(2-x) = 1.946*(5x+7)
    Solving for x,
    x = -0.9174

    Hope this helps :3

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