Explore BrainMass

Explore BrainMass

    Mathematics

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    4. Solve:
    a Solve for x if 2logx = 2 + log25
    b Simplify log3 81 - log3 27 + 4log3 v3
    c Find the inverse of the function f(x) = e^x + 1

    5. This is completing a piecewise function which consists of 2 straight lines and a parabola.
    Coordinates given are (-6,0) (-3,6)-straight line, (-3,6) (.5, -6) (2,-4) -parabola, and last straight line (2,-4) parallel to x-axis
    Need equation and domain for each piece

    © BrainMass Inc. brainmass.com December 15, 2022, 8:04 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/piecewise-function-straight-lines-parabola-269987

    Solution Preview

    Solution1a:
    Given: 2logx = 2 +log25
    log100 = 2 [Since, log100 = log102 = 2log10 =2]
    Therefore,
    2logx = log100 +log25
    Using power law of logarithms, 2log(x) = log(x2)
    Therefore,
    log(x2) = log(25) + log(100)

    Using sum rule for logarithms, log(25) + log(100) = log(25x100):
    log(x2) = log(2500)

    Removing all logarithms (by raising everything to the power of 10):
    x2= 2500
    Or, x = +/- 50

    Since 2log(-50) doesn't exist, therefore x = +50

    Solution1b:
    log3 81 = log81/log3 [Using the change of base rule for logarithms]
    = log 34/log3
    = 4log3/log3 [Using power law of ...

    Solution Summary

    This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.

    $2.49

    ADVERTISEMENT