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

Answered by A5T last updated on 13/Aug/24

$$a=2^x;b=2^y\Rightarrow a+b=18;\frac{a}{b}=5\Rightarrow a=5b$$$$\Rightarrow 6b=18\Rightarrow b=3\Rightarrow a=15$$$$2^{x+y}=ab=15\times 3=45$$

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

$$\mathrm{thank}\mathrm{you}$$

Answered by klipto last updated on 15/Aug/24

$$$$$$$$$$\mathbf{k}=2^{\mathbf{x}}\mathbf{p}=2^{\mathbf{y}}$$$$\therefore \mathbf{k}+\mathbf{p}=18$$$$\mathbf{and}\mathbf{from}\mathbf{indices}\mathbf{recall}$$$$2^{\mathbf{x}}\times 2^{\mathbf{y}}=\mathbf{kp}=2^{\mathbf{x}+\mathbf{y}}\mathrm{\&}{2}^{\mathbf{x}}\mathbf{÷}{2}^{\mathbf{y}}=\frac{\mathbf{k}}{\mathbf{p}}=2^{\mathbf{x}-\mathbf{y}}$$$$\mathbf{k}+\mathbf{p}=18,\frac{\mathbf{k}}{\mathbf{p}}=5,\mathbf{kp}=?$$$$\mathbf{k}=18-\mathbf{p}$$$$\mathbf{then}$$$$\frac{18-\mathbf{p}}{\mathbf{p}}=5,\mathbf{p}=3$$$$\mathbf{and}\mathbf{k}=18-3=15$$$$\therefore \mathbf{kp}=15\times 3=45✓$$$$\mathbf{klipto}-\mathbf{quanta}$$

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