8-x-2-x-6-x-3-x-2-find-x-Mastermind-

Question Number 170032 by Mastermind last updated on 14/May/22

\frac{8^{x} - 2^{x}}{6^{x} - 3^{x}} = 2, f i n d x ?

M a s t e r m i n d

Commented by Mastermind last updated on 14/May/22

y o u r s o l u t i o n p l e a s e

Commented by Rasheed.Sindhi last updated on 14/May/22

x = 1

Answered by Rasheed.Sindhi last updated on 14/May/22

\frac{8^{x} - 2^{x}}{6^{x} - 3^{x}} = 2, f i n d x ?

\frac{2^{x} (4^{x} - 1)}{3^{x} (2^{x} - 1)} = 2

\frac{2^{x} (2^{2 x} - 1)}{3^{x} (2^{x} - 1)} = 2

\frac{2^{x} (2^{x} - 1) (2^{x} + 1)}{3^{x} (2^{x} - 1)} = 2; 2^{x} \neq 1 \Rightarrow x \neq 0^{★}

\frac{2^{x} (2^{x} + 1)}{3^{x}} = 2

A s s u m i n g x a w h o l e n u m b e r

2^{x} \cdot \frac{2^{x} + 1}{3^{x}} = 2 = 1 \times 2

(2^{x} = 1 \land \frac{2^{x} + 1}{3^{x}} = 2) \lor (2^{x} = 2 \land \frac{2^{x} + 1}{3^{x}} = 1)

(2^{x} = 2^{0} \land \frac{2^{0} + 1}{3^{0}} = 2) \lor (2^{x} = 2^{1} \land \frac{2^{1} + 1}{3^{1}} = 1)

x \neq 0^{★}

H e n c e x = 1 (O n l y o n e s o l u t i o n i n w h o l e n u m b e r s)