algebra

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1. the function f(x)=6x/3x-5 is one to one. find its inverse and check your answer.

And on the second one can you tell me if I am correct.

2. solve the following exponential solution 7^2x+7^x+1-60=0

7^2 x+7^x-59=0
(49x)+7^x-59=0
49x/49=0/49
x=0/49
x=0

  • algebra -

    1.

    let y = 6x/(3x-5)
    the first step in finding the inverse is to interchange the x and y variables, so
    inverse is
    x = 6y/(3y-5)
    3xy - 5x = 6y
    3xy - 6y = 5x
    y(3x - 6) = 5x
    y = 5x/(3x-6) or f^-1 (x) = 5x/(3x-6)

    check with a point
    let x = 5 , then y = 30/(10) = 3

    plug 3 in for x in the inverse
    y = 15/(9-6) = 5 , looks good


    2. (not even close)

    I will assume you meant:
    7^(2x) + 7^(x+1) - 60 = 0
    7^(2x) + (7^1)(7^x) - 60 = 0
    let y = 7^x
    y^2 + 7y - 60 = 0
    (y+12)(y-5) = 0
    y = 5 or y = -12

    so
    7^x = 5 or 7^x = 12 , which would have no solution

    if y = 5
    7^x = 5
    log 7^x = log5
    xlog7 = log5
    x = log5/log7 = appr .827

    check:
    LS = 7^1.654 + 7^1.827 - 60
    = - .0144..
    not quite zero but close enough using only 3 decimal places for x
    try x = .827087475 and sub into the equation using your calculator.
    can't get any closer to 0 than that.

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