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Thread: Function/equation logarithmic

  1. #1
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    Cool Function/equation logarithmic

    Hi I have a few I am stumped on in my wonderful challenge of Algebra.

    First Problem is:

    Use the compound interest formulas
    A=P(1 + r over n)^nt and A=Pe^rt

    Suppose that you have $14,000 to invest. Which investment yields the greater return over 10 years: 7% compounded monthly or 6.85% compounded continuously?

    Second Problem:
    find the domain of each logarithmic function.
    F(x)=log(3-X)


    Third Problem:
    Solve each exponential equation by expressing each side as a power of the same base and then equating exponents.

    9^x = 1 over 27
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  2. #2
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    Quote Originally Posted by kbryant05

    Second Problem:
    find the domain of each logarithmic function.
    F(x)=log(3-X)


    Third Problem:
    Solve each exponential equation by expressing each side as a power of the same base and then equating exponents.

    9^x = 1 over 27
    Forgive me for not doing the first problem (interest problems make me angry).

    2)The logarithm $\displaystyle y=\log x$ its domain is, $\displaystyle x>0$ thus in the problem $\displaystyle y=\log (3-x)$ thus, $\displaystyle 3-x>0$ thus, $\displaystyle x<3$

    3)
    $\displaystyle 9^x=\frac{1}{27}$
    Note, $\displaystyle 9=3^2,27=3^3$ thus,
    $\displaystyle (3^2)^x=\frac{1}{3^3}$ use exponents rule,
    $\displaystyle 3^{2x}=3^{-3}$
    Thus,
    $\displaystyle 2x=-3$
    Thus,
    $\displaystyle x=-1.5$
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