Question-210605

Question Number 210605 by peter frank last updated on 13/Aug/24

Answered by A5T last updated on 13/Aug/24

a = 2^{x}; b = 2^{y} \Rightarrow a + b = 18; \frac{a}{b} = 5 \Rightarrow a = 5 b

\Rightarrow 6 b = 18 \Rightarrow b = 3 \Rightarrow a = 15

2^{x + y} = a b = 15 \times 3 = 45

Commented by peter frank last updated on 14/Aug/24

thank you

Answered by klipto last updated on 15/Aug/24

k = 2^{x} p = 2^{y}

∴ k + p = 18

and from indices recall

2^{x} \times 2^{y} = kp = 2^{x + y} & 2^{x} \div 2^{y} = \frac{k}{p} = 2^{x - y}

k + p = 18, \frac{k}{p} = 5, kp = ?

k = 18 - p

then

\frac{18 - p}{p} = 5, p = 3

and k = 18 - 3 = 15

∴ kp = 15 \times 3 = 45 ✓

klipto - quanta

Facebook Tweet Pin