Proofs
A proof is a series of claims that lead to a conclusion. Some proofs are conditional, which means that the claims can only be made under certain conditions. Click on a statement to see the proof
logb(x ⋅ y) = (logbx) + (logby)
x(m ⋅ n) = (xm)n
if n ⋅ p = m, then m = p ⋅ n
logb(xp) = p ⋅ (logbx)
logx(xp) = p
log2(23) = 3
if the following are true:
- x = i
- y = j
then i / j = x / y
if the following are true:
- x = i
- y = j
- z = k
- k = i / j
then z = x / y
logbx = (logcx) / (logcb)
log28 = (log108) / (log102)
if the following are true:
- a = b
- b = c
- c = d
- d = e
then a = e
if the following are true:
- a = b
- b = c
- c = d
- d = e
- e = f
then a = f
if the following are true:
- a = b
- b = c
- c = d
- d = e
- e = f
- f = g
then a = g
if the following are true:
- a = b
- b = c
- c = d
- d = e
- e = f
- f = g
- g = h
then a = h
a + ((-1) ⋅ a) = 0
if the following are true:
- a > b
- b > c
then a > c
if the following are true:
- a > b
- b = c
then a > c
if the following are true:
- a > b
- a = c
then c > b
if the following are true:
- a > b
- c = a
then c > b
if the following are true:
- a > b
- c = b
then a > c
if the following are true:
- a > b
- c = a
- d = b
then c > d
(a + b) ⋅ (b ⋅ (-1)) = ((a ⋅ b) ⋅ (-1)) + ((b ⋅ b) ⋅ (-1))
(b ⋅ a) + ((a ⋅ b) ⋅ (-1)) = 0
((a + c) + d) + b = ((b + c) + a) + d
if b + c = 0, then (a + b) + (c + d) = a + d
(a ⋅ a) + ((b ⋅ b) ⋅ (-1)) = (a + b) ⋅ (a + (b ⋅ (-1)))
(b / c) ⋅ c = (b ⋅ c) / c
if not (c = 0), then (b ⋅ c) / c = b
b(logbx) = x
if bm = bn, then m = n
if b > a, then b + c > a + c
(a + b) + (b ⋅ (-1)) = a
if x + 4 > 9, then x > 5
if y ⋅ 3 < 21, then y < 7
if y ⋅ (-2) < -16, then y > 8
if (x + 10) ⋅ (1 / (-5)) > 3, then x < -25
if (x + 10) / (-5) > 3, then x < -25
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