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Likurg_2 [28]
3 years ago
6

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

Mathematics
1 answer:
katen-ka-za [31]3 years ago
5 0

<u>We are given:</u>

aᵇ = bᵃ

b = 2a

<u>Finding (a+b):</u>

<u>Finding a:</u>

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]

<u>Finding b:</u>

We are given that b = 2a

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

b = 2(2)

b = 4

<u>Finding a+b:</u>

We found that a = 2, b = 4

a + b = 2 + 4 = 6

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