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College Algebra

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How do you solve 3 log(base 2)*(x-1)+ log(base 2)4=5

  • College Algebra - ,

    recall that n*log(a) = log(a^n)
    so, using base 2, we have

    3log(x-1)+log(4) = 5
    log(x-1)^3 + 2 = 5
    log(x-1)^3 = 3
    (x-1)^3 = 2^3
    x-1 = 2
    x = 3

    check:

    3log2 + log4 = 5
    3+2 = 5

  • College Algebra - ,

    another way would be

    3log(x-1)+log(4) = 5
    3log(x-1) + 2 = 5
    3log(x-1) = 3
    log(x-1) = 1
    x-1 = 2^1 = 2
    x = 3

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