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    Mathematics - Logarithmic and Exponential Functions

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    Practice Questions on Logarithmic and Exponential Functions

    [See the Attached Questions File]

    Evaluate the logarithm:

    log4(1/16)

    Evaluate the logarithm:

    log10(0.01)

    Evaluate the logarithm:

    log1/2(5)

    Sketch the graph of the function and identify the vertical asymptote:

    f(x) = -2 + log3x

    Use the properties of logarithms to expand the expression:

    Use the properties of logarithms to condense the expression:
    4(1 + ln x + ln x)
    Use the properties of logarithms to condense the expression:
    ln (x + 4) - 3 ln x - ln y
    Solve the equation:
    3^x=500
    Find the value of this?
    100e^-0.6=

    Solve the equation:
    2log4 x -log4(x-1)=1

    A deposit of $5000 is placed in a savings account for 2 years. The interest for the account is compounded continuously. At the end of 2 years, the balance in the account is $5751.37. What is the annual interest rate for this account?

    Find the annual interest rate:
    Principal Balance Time Compounding
    $5000 $15,399.30 15 years Daily

    . Find the annual interest rate:
    Principal Balance Time Compounding
    $7500 $15,877.50 15 years Continuous

    Find the effective yield:
    Rate Compounding
    5.5% Daily

    $ 100 becomes 100[1 + 0.055/365]^365 in one year. This evaluates to $ 105.65 in one year. Thus, interest earned is $ 5.65. Yield = interest/investment = 5.65/100 = 0.056
    in one year.

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    Attachments

    Solution Preview

    Please see attached file for solutions to the Practice Questions on Logarithmic and Exponential
    Functions.

    Evaluate the logarithm:

    = log (1/16) / log 4 = log [4^-2] / log 4 = -2.log 4 / log 4 = -2.

    Evaluate the logarithm:

    = log 0.01 / log 10 = log [10^-2] / log 10 = -2.log 10/log 10 = -2.

    Evaluate the logarithm:

    = log 5 / log (1/2) = log 5 / log [2^-1] = log 5 / -1.log 2 = - log 5 / log 2 = - 2.32.
    Sketch the graph of the function and identify the vertical asymptote:

    The graph is shown below. The vertical asymptote is the y - axis, whose equation
    is x = 0. [Go and see the next page if required].

    Use the properties ...

    Solution Summary

    Complete, Neat and Step-by-step Solutions to the Practice Questions are provided in the attached file.

    $2.19

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