Math Problem 4(lnx)^2 = lnx^2?

anonymousanonymous
in Science & Mathematics

I can't figure out how to solve this problem. My book says I need to answer the problem exactly without using a calculator.

The problem is : 4(lnx)^2 = lnx^2

Help would be really appreciated!

Comments

  • mein-hoon-namein-hoon-na

    we know ln (a^y) = y ln a

    so 4(ln x)^2 = ln x^2 = 2 ln x

    or 2 ln x = 1

    or ln x = 1/2

    or x = e^(1/2)

  • markmark

    4(lnx)² = lnx²

    Bring the exponent in the proudt out as an coefficient:

    4(lnx)² = 2lnx

    divide both sides by (lnx)²:

    4 = 2lnx / (lnx)²

    lnx reduces out in the numerator since it is a factor in the numerator and denominator:

    4 = 2/ lnx

    cross multiply:

    4lnx = 2

    divide both sides by 4:

    lnx = 2/4

    reduce the fraction:

    lnx = 1/2

    change to exponential form:

    e^(1/2) = x

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