One-to-One Property

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 8, 2021.

  1. nycmathguy

    nycmathguy

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    Section 3.1

    The One-to-One Property states

    For a > 0 and a ≠ 1, a^x = a^y
    if and only if x = y.

    Use the One-to-One Property to solve the equation for x.

    a. 8 = 2^(2x−1)

    b. (1/3)^(-x) = 27

    Part (a)

    I have to rewrite 8 having a base 2.

    Let 8 = 2^3

    I can now apply the One-to-One Property.

    2^3 = 2^(2x - 1)

    3 = 2x - 1

    3 + 1 = 2x

    4 = 2x

    4/2 = x

    2 = x

    Yes?

    Part (b)

    (1/3)^(-x) = 3^x.

    3^x = 27

    Let 27 = 3^3.

    3^x = 3^3

    Bases are the same. Bring down exponents.

    x = 3

    Yes?
     
    nycmathguy, Oct 8, 2021
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  2. nycmathguy

    MathLover1

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    correct
     
    MathLover1, Oct 8, 2021
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  3. nycmathguy

    nycmathguy

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    Are exponential and logarithmic functions opposite operations?
     
    nycmathguy, Oct 8, 2021
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  4. nycmathguy

    MathLover1

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    Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = log(a, x ) is defined to be equivalent to the exponential equation x = a^y.
     
    MathLover1, Oct 8, 2021
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  5. nycmathguy

    nycmathguy

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    Thank you. I think logarithmic functions is the next section.
     
    nycmathguy, Oct 8, 2021
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