Equation

kreshnik · **Joined:** Sun, 25 Dec 2011 00:28:25 UTC **Posts:** 95

Is given

$$m=\frac{2^a+6^a+8^a}{1+3^a+4^a}\;\;\;,\;\;a\in N\;\;\text{which number below can be m?}$

$$A)\;18\;\;\;B)\;72\;\;\;C)\;100\;\;D)\;256$

$$m=\frac{2^a+6^a+8^a}{1+3^a+4^a}=\frac{2^a(1+3^a+4^a)}{1+3^a+4^a}=2^a\;\;=>\;m=2^a$

$\text{If:}$

$$a=1\;\;=>\;m=2$

$$a=2\;\;=>\;m=4$

$$a=3\;\;=>\;m=8$

$$a=4\;\;=>\;m=16$

$$a=5\;\;=>\;m=32$

$$a=6\;\;=>\;m=64$

$$a=7\;\;=>\;m=128$

$$a=8\;\;=>\;m=256$

$$a=9\;\;=>\;m=512$

...if I'm right, D should be the correct answer. But I want to know if there's any other way of doing this or not.

Thank you.

Denis · **Posted:** Sun, 15 Jan 2012 15:30:46 UTC

log(18) / log(2) = ~4.17
log(72) / log(2) = ~6.17
log(100)/ log(2) = ~6.64
log(256)/ log(2) = 8.000000000000000000000000000000000000000000.......

kreshnik · **Joined:** Sun, 25 Dec 2011 00:28:25 UTC **Posts:** 95

Denis wrote:

log(18) / log(2) = ~4.17
log(72) / log(2) = ~6.17
log(100)/ log(2) = ~6.64
log(256)/ log(2) = 8.000000000000000000000000000000000000000000.......

I guess you're angry with those zeros about something. :!:

You know what, I was thinking about your advice, wristwatch should be perfect, but only a temporary one, with ball pen :lol:

Thanks.

outermeasure · **Posted:** Sun, 15 Jan 2012 23:51:55 UTC

kreshnik wrote:

Denis wrote:

log(18) / log(2) = ~4.17
log(72) / log(2) = ~6.17
log(100)/ log(2) = ~6.64
log(256)/ log(2) = 8.000000000000000000000000000000000000000000.......

I guess you're angry with those zeros about something. :!:

You know what, I was thinking about your advice, wristwatch should be perfect, but only a temporary one, with ball pen :lol:

Thanks.

Really, small perfect powers (e.g. those below 1000), or failing that, small perfect prime powers, should be memorised.

S.O.S. Mathematics CyberBoard

Equation

Who is online