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# Algebra and Functions - Inequelities

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1. 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 ?
2. 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
3. (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.
4. Thank You !!!

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Updated: July 9, 2016
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