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Math Help - Find 10^(k + 3)

  1. #1
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    Find 10^(k + 3)

    Although I'm now in calculus, our professor wants to make sure that students do not forget the important topics of pre-calculus. To reach this goal, in addition to our calculus 1 homework, the professor adds one or two problems from pre-calculus as extra homework. Below is a problem that I worked on for about 15 minutes. Each time, I got the answer of 1000 but the correct answer is 500.

    QUESTION:

    If 10^(k) = 1/2, find 10^(k + 3)

    How do I get 500 here?

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  2. #2
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    Quote Originally Posted by magentarita View Post
    Although I'm now in calculus, our professor wants to make sure that students do not forget the important topics of pre-calculus. To reach this goal, in addition to our calculus 1 homework, the professor adds one or two problems from pre-calculus as extra homework. Below is a problem that I worked on for about 15 minutes. Each time, I got the answer of 1000 but the correct answer is 500.

    QUESTION:

    If 10^(k) = 1/2, find 10^(k + 3)

    How do I get 500 here?
    10^{k+3}=10^k\times10^3

    =\frac{1}{2}\times1000
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  3. #3
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    ok...

    Quote Originally Posted by mathaddict View Post
    10^{k+3}=10^k\times10^3

    =\frac{1}{2}\times1000
    Of course, 1/2 times 1000 = 500

    I thank you for the set up but here is what I did:

    If 10^(k) = 1/2, find 10^(k + 3)

    I multiplied both sides by denominator 2 to remove the fraction on the right side.

    2(10^(k)) = 1

    20^(k) = 1

    At this point, I concluded that k has to be 0 because anything raised to the zero power = 1.

    I then replaced k with zero for 10^(k + 3) = 10^3 = 1000

    Did you follow what I did wrong?

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  4. #4
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     <br />
10^(k+3)= 10^k \times 10^3 = \frac{1}{2} \times 1000<br />

    2(10^(k)) = 1..........correct

    20^(k) = 1....................This is not correct
    Find the reason
    .................

    2(10^{k}) = {(2^\frac{1}{k} \times 10)}^k
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  5. #5
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    Quote Originally Posted by magentarita View Post
    Of course, 1/2 times 1000 = 500

    I thank you for the set up but here is what I did:

    If 10^(k) = 1/2, find 10^(k + 3)

    I multiplied both sides by denominator 2 to remove the fraction on the right side.

    2(10^(k)) = 1

    20^(k) = 1

    At this point, I concluded that k has to be 0 because anything raised to the zero power = 1.

    I then replaced k with zero for 10^(k + 3) = 10^3 = 1000

    Did you follow what I did wrong?
    Oh alright .

    Note that 2(10^k) is NOT equal to 20^k . THat's a big mistake .
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