missing exponent

[aharvey]

This is pretty simple and straight forward, I am having some trouble figuring this out.
Find the missing exponent
(4x^5)?= 1

Its x to the fifth power by the way and the question mark is asking what is the missing exponent.
How can this be true?

 

[BigGlenntheHeavy]

\(\displaystyle (4x^5)^0 \ = \ 1, \ x \ \ne \ 0.\)

 

[lookagain]

This is pretty simple and straight forward, I am having some trouble figuring this out.
Find the missing exponent
(4x^5)?= 1

Its x to the fifth power by the way and the question mark is asking what is the missing exponent.
How can this be true?

aharvey,

\(\displaystyle if \ x = \frac{1}{\sqrt[5]{4}}, \ then \ the \ missing \ exponent \ can \ be \ any \ real \ number.\)

 

[BigGlenntheHeavy]

\(\displaystyle 1^i \ = \ 1, \ i \ = \ \sqrt{-1}\)

\(\displaystyle Proof: \ Let \ 1^i \ = \ k, \ then \ i[ln(1)] \ = \ ln|k|, \ i(0) \ = \ ln|k|,\)

\(\displaystyle \implies \ln|k| \ = \ 0, \ k \ = \ e^0, \ k \ = \ 1, \ QED.\)

\(\displaystyle 1^x \ = \ 1, \ then \ the \ missing \ exponent \ x \ can \ be \ any \ number, \ real \ or \ imaginary.\)

 

[Denis]

\(\displaystyle 1^i \ = \ 1, \ i \ = \ \sqrt{-1}\)

\(\displaystyle Proof: \ Let \ 1^i \ = \ k, \ then \ i[ln(1)] \ = \ ln|k|, \ i(0) \ = \ ln|k|,\)

\(\displaystyle \implies \ln|k| \ = \ 0, \ k \ = \ e^0, \ k \ = \ 1, \ QED.\)

\(\displaystyle 1^x \ = \ 1, \ then \ the \ missing \ exponent \ x \ can \ be \ any \ number, \ real \ or \ imaginary.\)

Hey nice one, BigG; today is a good day, cause I learned something :wink:

 

[Deleted member 4993]

I suppose Ted has taken some action - but has not removed the offending posts. I am going to remove those posts and all the references to those posts