Question

Let 2^a+b=10,2^b+c=20 and 2^c+a=30,where a,b and c are any real numbers.the value of 2^a is

Answer 1

Step-by-step explanation:

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Answer 2

$2^{a} = \sqrt{15}$

Step-by-step explanation:

Given that, $2^{(a + b)} = 10$ ............ (1)

and, $2^{(b + c)} = 20$ ............. (2)

and, $2^{(c + a)} = 30$ .............. (3)

Now, multiplying the three equations, we get

$2^{(a + b) + (b + c) + (c + a)} = 10 \times 20\times 30$

⇒ $2^{2(a + b + c)} = 6000$

⇒ $2^{(a + b + c)} = \sqrt{6000} = 20\sqrt{15}$ .............. (4)

Now, dividing equation (4) by equation (2), we get

$2^{(a + b + c) - (b + c)} = \frac{20\sqrt{15}}{20}$

⇒ $2^{a} = \sqrt{15}$ (Answer)