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Math help

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Where appropriate, include the approximation to the nearest ten-thousandth.

31.) log(x-4)+ log(x+4)= log4
I have the answer as 4

Is this answer right?

  • Math help -

    log a + log b is same as log ab

    so log(x^2-4)=log4
    taking antilogs
    x^2-4=4 solve for 4
    check my thinking.

  • Math help -

    Okay x^2-4 = 4

    x^2= 8

    sqrt(x^2)= sqrt 8

    x= 2.83 is this right?

  • Math help -

    log k has a nasty habit of becoming undefined if k is not positive.

    you answer of x = 2.832 is correct according to the steps taken, but...

    when we sub into log (x-4) we get log (-1.168 which is undefined,

    so there is no solution in the set of real numbers for your equation

  • Correction: Math help -

    Going back and looking over the previous solutions, I noticed that the original non-log equation should have said:

    x^2-16 = 4
    so x^2 = 20
    x = √20 = 4.472136

    which works upon substituting.

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