if 1 power 0=1 and 1 power 45=1,shall we say 0=45(not only 45 but also any +ve no.)?

Question

This question may seem funny. i used o get such vague doubts. it'd be better if this is answered by any proofs and Eminent teachers.

Answer 1

DO YOUR OWN HOME WORK

Answer 2

Anything to the zero power is 1, except 0. None of this has anything to do with concluding that 0= 45.What would you rather have, 0 dollars or 45 dollars?

Answer 3

1^0 = 1
1^45 = 1

Although it is true that

1^0 = 1^45

We cannot equate the exponents like we do for variables. The reason is because we cannot take the log of both sides like we normally do to solve equations like these;

ln(1^0) = ln(1^45)
0 ln(1) = 45 ln(1)

The problem is, ln(1) = 0 so we can't really divide both sides by ln(1) to conclude 0 = 45.

Answer 4

Do logs of base one exist?

1^0 = 1^45

log(base 1)(1^0) = ln(1^0)/ln 1 = 0/0.

Answer 5

Why would it be?

Try to explain why it would be and see where you stumble.

That will show you why it's not true.

Often, the best way to find a proof of the truth is to try to find a proof of the opposite (false) statement and see where the attempt fails.

Answer 6

1^0 = 1
1^45 = 1

why whould you conclude now that 0 = 45 ???????

its not funny its plain stupid.

Answer 7

Addition and multiplication are "commutative".
"To the power of" is not.

For your proof to work, the operand must be
commutative, and it isn't.