1
Q
form inequality for approximations and contradictions
A
log(a)(b) = 1/log(b)(a)
2
Q
log(a)(x) is the inverse of
A
a^x
3
Q
a^log(a)(x) = x
A
log(a)(b) < c –> b < a^c
4
Q
3(root3) < 4
A
27 < 16
contradiction
therefore 3(root3)>4
5
Q
log_a_b < c –>
A
b < a^c
6
Q
Comparing logs:
A
Change bases, form inequalities, make approximations where appropriate, form inequalities by considering the approximations
7
Q
Log(a) < 0 when
A
a < 1
8
Q
log(a)(b) =
A
log(c)(b) / log(c)(a) === 1/log(b)(a)
9
Q
Log1 =
A
0
10
Q
a^ (log(a)x) =
A
log(a)(a^x) = x
11
Q
change bases on largest log values and
A
find contradiction
12
Q
a^loga(b) =
A
b
13
Q
log(2)(3) > 1.5 therefore
A
2^1.5 < 3
14
Q
logab < c
A
Raise both sides to the base of the log, a
a^logab < a^c
LHS = b
Therefore a^c > b
