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    1. State the smallest integer n for which 5n>31.

    2. What integer values of x satisfy 100<4^x<10 000?


    Can anyone help out please ?
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    1. 5n>31 so divide both sides by 5
    n>31/5


    2. 100<4^x<10000

    100<4^x
    xlog4>log100
    x>log100/log4

    xlog4<log10000
    x<log10000/log4
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    (Original post by Rutha)
    1. State the smallest integer n for which 5n>31.

    2. What integer values of x satisfy 100<4^x<10 000?


    Can anyone help out please ?
    1. Divide both sides my 5 and round the answer UP to get the smallest integer.

    2. First find the lower bound by doing 100<4x and round it up to the nearest integer - A.

    Then find the upper bound by doing 4x<10000 and round it down to the nearest integer - B.

    Your range is A<x<B for all integers x.

    The key here is to isolate the x then check for integers on either side of your answer to see if it fits within the range; hence rounding up/down.
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    Thank You !!!
 
 
 
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