Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

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

Noura11Best ResponseYou've already chosen the best response.0
Wait ! a should be a positive real !
 9 months ago

mitodoteiraBest ResponseYou've already chosen the best response.0
a>1 I forgot to say that. Facepalm.
 9 months ago

Noura11Best ResponseYou've already chosen the best response.0
It is true for all a>0. We can say : \[\Large a^ba^c=e^{\ln a^b}e^{\ln a^c}\\ ~~~~~~~~~\Large =e^{b\ln a}e^{c\ln a}\\ ~~~~~~~~~\Large=e^{b\ln a+c\ln a}\\ ~~~~~~~~~~\Large=e^{(b+c)\ln a}\\ ~~~~~~~~~~\Large=e^{\ln a^{b+c}} \\ ~~~~~~~~~~\Large=a^{b+c}\]
 9 months ago

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

Noura11Best ResponseYou've already chosen the best response.0
OK ! If b and c are natural integers you can prove it using induction !
 9 months ago

mitodoteiraBest ResponseYou've already chosen the best response.0
b, c are just real.
 9 months ago

Noura11Best ResponseYou've already chosen the best response.0
@mitodoteira My last reply is the 1st step of the proof !
 9 months ago

sauravshakyaBest ResponseYou've already chosen the best response.0
I dont think we can use induction here... three variables
 9 months ago

sauravshakyaBest ResponseYou've already chosen the best response.0
Isnt 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.
 9 months ago

mitodoteiraBest ResponseYou've already chosen the best response.0
No, it isn't a property.
 9 months ago

swissgirlBest ResponseYou've already chosen the best response.0
hmmmmm how do you define the exponential function?
 9 months ago

swissgirlBest ResponseYou've already chosen the best response.0
http://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.
 9 months ago
See more questions >>>
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.