ab ≠o means that neither a nor b is 0
question, does a = b?
$$statement\ 1:\ x^a\ =\ x^b$$
$$if\ x\ =\ 0,\ a\ =\ 1\ and\ b\ =\ 1$$
$$0^1\ =\ 0^1$$
0 = 0 {This is wrong because ab ≠0}
if x = 1, a = 1 and b = 1
$$1^1\ =\ 1^1$$
1 = 1 {a = b}
if x = 2, a = 2 and b = 3
$$2^2\ =\ 2^3$$
4 = 8
Statement 1 is not sufficient because there is a lot of combination that proves that a ≠b
Statement 2: x /a/ = x /b/
We cannot divide this equation by x to get /a/ = /b/ unless x = 0
Even if we have /a/ = /b/ our answer would be either a = b, a = -b, -a = -b or
-a = b, statement 2 is not sufficient to prove that a = b .
Answer = E because both statement are not sufficient.
If ab ≠0, does a=b?
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Since ab ≠0, that means neither a nor b is 0. We need to determine whether a = b.VJesus12 wrote:If ab ≠0, does a=b?
(1) x^a = x^b
(2) x|a| = x|b|
Statement One Alone:
x^a = x^b
If x = 2, then a = b. However, if x = 1, then a and b could be any numbers. For example, a could be 1 and b could be 2.
Statement one alone is not sufficient.
Statement Two Alone:
x|a| = x|b|
We see that a could equal b; for example, x = 1 and a = b = 1. However, a could also not equal b, for example, x = 1, a = 1 and b = -1.
Statement two is not sufficient.
Statements One and Two Together:
With the two statements, we still can't determine whether a = b.
For example, x = 1 and a = b = 1 or x = 1, a = 1 and b = -1 and thus a does not equal b.
Answer: E
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