college algebra

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Solve the logarithmic equation.

Log x +log2x = 4

Wouldn't this be no solution because log x is undefined?

  • college algebra -

    logx + log 2x = 4
    log (x(2x)) = 4 , using the rule log AB = logA + logB
    log (2x^2) = 4
    so 2x^2 = 10^4
    2x^2 = 10000
    x^2= 5000
    x = ± √ 5000
    but x > 0 for log x to be defined

    so x = √5000

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