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Math Help - ALGEBRA URGENT!! thank you

  1. #1
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    ALGEBRA URGENT!! thank you

    7 10^6 divided by a 10^n is equal to 8.75 10^9
    a is greater or equal to 1 but less than 10.
    Find the value of a and the value of n.
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  2. #2
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    Solution involves logs and inequalities.

    (7X10^6)/(aX10^n) = 8.75X10^9 where a>=1 and a<10.

    7X10^6 = aX10^n X 8.75X10^9

    1/8.75 = aX10^(n+9-6)

    0.8 = aX10^(n+3)

    8/10 = aX10^(n+3)

    8 = aX10^(n+3) X 10^1

    8 = aX10^(n+3+1)

    8 = aX10^(n+4)

    a = 8/[10^(n+4)]

    a>=1

    8/[10^(n+4)]>=1

    8>=10^(n+4)

    log8>=log10^(n+4)

    log8>=(n+4)log10

    log8>=(n+4)(1) (since log10 =1)
    log8>=n+4
    log8-4>=n
    -3.096910013>=n

    or

    a<10

    8/[10^(n+4)]<10

    8<10X10^(n+4)

    8<10^(n+4+1)

    8<10^(n+5)
    log8<log10^(n+5)
    log8<(n+5)log10
    log8<(n+5)(1) (since log10 = 1)

    log8<n+5
    log8-5<n
    0.4771212547<n

    (I am not sure if the above solution is correct. It seems too involved. I feel that there might be an easier solution. I sure would like to know what it is. Cheers Abey.
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  3. #3
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    Sorry this is late abey, but hope it helps...

    7 x 10^6 = 8.75 x 10^9
    a x 10^n

    multiply through by a x 10^n, so you get:

    7 x 10^6 = a x 10^n
    8.75 x 10^9

    therefore a = 7/8.75=0.8

    and n = 6-9 = -3
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  4. #4
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    Quote Originally Posted by thegarden View Post
    Sorry this is late abey, but hope it helps...

    7 x 10^6 = 8.75 x 10^9
    a x 10^n

    multiply through by a x 10^n, so you get:

    7 x 10^6 = a x 10^n
    8.75 x 10^9

    therefore a = 7/8.75=0.8

    and n = 6-9 = -3
    EDIT: I have just re-read the question. It states: a is greater or equal to 1 but less than 10. So i am not sure if my solution is correct.
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  5. #5
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    I think i have the correct solution now:

    working through it again...

    7 x 10^6 = 8.75 x 10^9
    a x 10^n

    multiply through by a x 10^n, so you get:

    7 x 10^6 = a x 10^n
    8.75 x 10^9

    Simplifying, 0.0008 = a x 10^n

    0.0008 is the same as 8 x 10^-4

    So a=8 and n = -4
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