Algebra Exponential and Sums & Difference of Logarithmic Questions

  1. Determine whether the given functions are one-to-one. It they are one-to-one, find a formula for the inverse.(a) LaTeX: fleft(xright)=-x+5

    f



    (


    x


    )



    =





    x


    +


    5

    (b) LaTeX: fleft(xright)=x^2-4


    f



    (


    x


    )



    =



    x


    2






    4

    (c) LaTeX: fleft(xright)=2x^3-5


    f



    (


    x


    )



    =


    2



    x


    3






    5

    (d) LaTeX: fleft(xright)=sqrt{x-5}


    f



    (


    x


    )



    =



    x





    5


    (e) LaTeX: fleft(xright)=frac{6}{x+5}


    f



    (


    x


    )



    =



    6



    x


    +


    5



  2. Answer the following exponential and logarithmic questions(a) Use properties of logarithms to expand the logarithmic expression, LaTeX: logleft(10,000x^2right)

    log






    (



    10


    ,


    000



    x


    2




    )


    Then simplify.(b) Solve the equation LaTeX: 3^x=81



    3


    x



    =


    81

    (c) Solve the equation LaTeX: log_6left(x+2right)=2



    log


    6







    (



    x


    +


    2



    )



    =


    2

    (d) Express in terms of sums and difference of logarithms LaTeX: log_bleft(6x^5yz^2right)



    log


    b







    (



    6



    x


    5



    y



    z


    2




    )


    (e) Expand and simplify LaTeX: lnleft(2e^3right)

Maybe one or two problems on graphing