The Quasi-Sequence

If y = 10^x, then...

Brain saying "WOW!"

x	y
0	1
log 2	2
log 3	3
log 4	4
log 5	5
log 6	6
log 7	7
log n	n

(log 1 = 0) But if n < or = 0, this trick won't work. In other words, it only works if n is positive.

But wait, there's more!

x	y
1	2
log23	3
2	4
log25	5
log2n	n

y = 2^x

x	y
1	5
log56	6
log57	7
log58	8
log5n	n

y = 5^x

x	y
0	1
1/3	2
log83	3
2/3	4
log8n	n

y = 8^x

x	y
0	1
logT2	2
logT3	3
logTn	n

y = T^x (T ≠ 0 or 1; assume T is positive.)

logaa = 1 (a ≠ 0 or 1; loga1 = 0; assume a is positive.)

Amazing, isn't it?

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© Derek Cumberbatch