Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

If a^b= b^a and b = 2a, what is the value of a + b?​

Sagot :

TheSection

We are given:

aᵇ = bᵃ

b = 2a

Finding (a+b):

Finding a:

replacing b by 2a in the first equation, we get:

(a²)ᵃ = (2a)ᵃ

(a²)ᵃ = 2ᵃ * aᵃ

a²ᵃ / aᵃ = 2ᵃ                  [dividing both sides by aᵃ]

aᵃ = 2ᵃ                          [because xᵃ / xᵇ = xᵃ⁻ᵇ]

a = 2                             [raising both sides to 1/a]

Finding b:

We are given that b = 2a

now that we know what a equals, we will plug that value here

b = 2(2)

b = 4

Finding a+b:

We found that a = 2, b = 4

a + b = 2 + 4 = 6

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.