Question

1/2^n < 0.01
what is the value of n

Answer 1

\[\frac{1}{2^{n}}<0.01\]
Is this it?

Answer 2

yes sir

Answer 3

Do you want to take it step by step? The first step being to multiply both sides by 2^n.

Answer 4

step by step will be more helpful

Answer 5

Lets do it step by step. Can you multiply both sides by 2^n and post your result?

Answer 6

2^n < 0.01(2^n)

right?

Answer 7

Not quite.
\[\frac{1}{2^{n}}\times\frac{2^{n}}{1}=?\]

Answer 8

ok...

Answer 9

then?

Answer 10

1 < (0.01)(2^n)

Answer 11

Good work! The next step is to take logs of both sides of equation (1)
\[1<0.01\times2^{n}\ .........(1)\]

Answer 12

log 1 < log (0.01)(2^n)

Answer 13

0 < Log (0.01) + log 2^n

Answer 14

Yes, but we can take the right hand side a step further:
\[\log\ 1<\log\ 0.01+n\ \log\ 2\ .......(2)\]

Answer 15

got it... what will be the next step??

Answer 16

Subtract log 0.01 from both sides.

Answer 17

2 < n log 2

Answer 18

???

Answer 19

You are correct. Now divide both sides by log 2.

Answer 20

ok sir thanks a lot

Answer 21

You're welcome :)

Answer 22

Of course if you take n to be an integer, as a child of the digital age you know the powers of 2 by heart. 128 (the 7th power) fits the bill so the 1/128 < .01. The sixth power doesn't.

Answer 23

\[n >\frac{2}{\log\ 2}=6.644\]