It's very straight forward: 5^3 = 125, so we can approximate 5^100 to 125^33.3 2^7 = 128, so we can approximate 2^234 to 128^33.5 Now it's obvious that 128^33.5 > 125^33.3, so 2^234 > 5^100
I multiplied with 2^100 to get 2^(234+100) = 2^334 and 5^100*2*100 = 10^100. So is 2^334 bigger than 10^100? 2^10= 1024. Thats 3 digits more than 2^0=1. So every power of 10 we win slightly more than 3 digits as our result is not exactly 1000 but bigger. 334/10 means we do that 33,4 times. 3*33,4=100,2. So we have a bit more than 100,2 digits or 10^100. This would lead me to 2^234 > 5^100. Was my way correct?
or you could have memorized Log for the first 10 numbers to a few digits and solved it like an engineering student. (also why having a slide ruler was often better than a simple 4 function calculator)
It's very straight forward:
5^3 = 125, so we can approximate 5^100 to 125^33.3
2^7 = 128, so we can approximate 2^234 to 128^33.5
Now it's obvious that 128^33.5 > 125^33.3, so 2^234 > 5^100
Just watched and seen that's what the video ends with, but with a lot of unnecessary meandering beforehand
2^{334} vs 10^100; 2^3.34 vs 10; 2^{10/3} vs 10; 2^10 vs 1000; 1024 vs 1000, so 2^234>5^100
Check 234*ln2=162.196... and 100*ln5=160.944...
I multiplied with 2^100 to get 2^(234+100) = 2^334 and 5^100*2*100 = 10^100.
So is 2^334 bigger than 10^100?
2^10= 1024. Thats 3 digits more than 2^0=1. So every power of 10 we win slightly more than 3 digits as our result is not exactly 1000 but bigger. 334/10 means we do that 33,4 times. 3*33,4=100,2. So we have a bit more than 100,2 digits or 10^100.
This would lead me to 2^234 > 5^100.
Was my way correct?
or you could have memorized Log for the first 10 numbers to a few digits and solved it like an engineering student. (also why having a slide ruler was often better than a simple 4 function calculator)
1^1^3^2^2 vs5^10^10 1^1^2vs5^2^5^2^5 1^2vs1^1^1^2^1 (x ➖ 2x+1). 1^2vs2^1 (x ➖ 2x+1) 2^234 >5^100
The task is more difficult 5^51 or 2^118 ?
Very simple 5^100 = 2°232,2 therefore its clearly < than 2^234
Just how did you conclude that?
@@okaro6595 I have to admit I used a calculator. log5/log2 = 2,3219 (2,322).
2^2,332= 5, therefore 5^100 has to be 2^(100x2,322)
Ill say 5^100