Question

For any real number a > 0, with a not equal to 1, which of the following properties is not always true?
A. a^x is a unique for any real number x
B. a^b = a^c if and only if b = c
C. For m < n, we have a
^m < a^n.
D. None of the above

Last one, friends. I am tallying my answers in my homework with yours. thank you so much for the help! :)

Answer 1

the answer is B

Answer 2

why?

Answer 3

B is logically true
if b=c

a^b = a^b replace b=c in the right part
so
a^b = a^c

Answer 4

but what about item A?

Answer 5

for any real number x!!
so if you take x=2 then x=3

is a^2 = a^3 ?! for a not equal to 1

Answer 6

alright. thanks so much, hoblos. :)

Answer 7

glad to help XD