A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Prove: a^b*a^c=a^(b+c) for real a, b, c.
anonymous
 3 years ago
Prove: a^b*a^c=a^(b+c) for real a, b, c.

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[a,b,c \in \mathbb{R}\]\[Prove: a^{b}a^{c}=a^{b+c}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Wait ! a should be a positive real !

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0a>1 I forgot to say that. Facepalm.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It is true for all a>0. We can say : \[\Large a^ba^c=e^{\ln a^b}e^{\ln a^c}\\ ~~~~~~~~~\Large =e^{b\ln a}e^{c\ln a}\\ ~~~~~~~~~\Large=e^{b\ln a+c\ln a}\\ ~~~~~~~~~~\Large=e^{(b+c)\ln a}\\ ~~~~~~~~~~\Large=e^{\ln a^{b+c}} \\ ~~~~~~~~~~\Large=a^{b+c}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I can't use logs. I'm doing analysis and I'm still proving the fundamentals of real powers from the field axioms.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0OK ! If b and c are natural integers you can prove it using induction !

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@mitodoteira My last reply is the 1st step of the proof !

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I dont think we can use induction here... three variables

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Isnt it the property??? I am not sure if it can be proven. example : we know a*b=b*a because its a property what how to Prove it.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0No, it isn't a property.

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0hmmmmm how do you define the exponential function?

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0http://math.stackexchange.com/questions/435751/provingtheproductruleforexponentswiththesamebase Here is the link to this particular question I asked on MSE. Take a look at both proofs. The proof using Least Upper Bound is more analytical and a touch harder to follow but I think that is the proof you are looking for.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.