Using a simple hand calculator with pen and paper, and without direct evaluation, determine which of these quantities is greater.
2142 or 945
*** You can use computer program/excel solver only for purposes of verification.
I will try to lean back on my memorized table of 2-digit common logarithms:
log(2) = .30
log(3) = .48
but log(9) = .95 by interpolation between 3*log(2) and log(10).
142*.30 = 42.6
45*.95 = 42.75
It's a really close call; using log(3), 45*.48*2 = 43.2 makes it a little more distant, not very, especially considering it's not quite as accurate, but it does seem that 9^45 is somewhat larger than 2^142.
Comparing to actual calculation:
>> 2^142
ans =
5.57518629963266e+42
>> 9^45
ans =
8.72796356808771e+42
and indeed 9^45 is larger than 2^142.
Full log table reconstructed from memory:
2 .30
3 .48 (first two are pure memory)
4 .60 (2*2)
5 .70 (10/2)
6 .78 (3*2)
7 .85 (interpolation adjusted for declining slope)
8 .90 (2^3)
9 .95 (interpolation between 8 and 10)
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Posted by Charlie
on 2023-08-12 09:01:05 |
my method
