If-log-2-9-x-1-7-log-2-3-x-1-1-2-then-the-values-of-x-are-

Question Number 19382 by chernoaguero@gmail.com last updated on 10/Aug/17

If \log_{2} (9^{x - 1} + 7) - \log_{2} (3^{x - 1} + 1) = 2,

then the values of x are

Answered by khamizan833@yahoo.com last updated on 10/Aug/17

x = (1, 2)

Answered by ajfour last updated on 10/Aug/17

let 3^{x} = t

\Rightarrow \frac{\frac{t^{2}}{9} + 7}{\frac{t}{3} + 1} = 4

t^{2} + 63 = 12 t + 36

t^{2} - 12 t + 27 = 0

(t - 3) (t - 9) = 0

\Rightarrow t = 3^{x} = 3, 9

\Rightarrow x = 1 or x = 2 .

Commented by chernoaguero@gmail.com last updated on 10/Aug/17

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