Question:

Solving a logarithmic equation?

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2 * 3^(x+5) = 3^(2x) + 3^10

How would you solve this equation for x?

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  1. Greetings

    2*3^5*3^x = (3^x)^2 + 3^10

    Let z = 3^x

    486z = z^2 + 59049

    z^2 - 486z + 59049 = 0

    By the quadratic formula,

    z = (486 +/- sqrt(486^2 - 4*59049))/2

    z = 243

    3^x = 243

    xlog3 = log243

    x = log243/log3

    x = 5

    Check

    2*3^(5 + 5) = 3^(2*5) + 3^10

    2*3^10 = 2*3^10

    Regards

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