Question

If 27^x= 9 / 3^x find the value of x.

Answer 1

hello mate.....

given......

$27 {}^{x} = \frac{9}{3 {}^{x} } \\ \\ 27 {}^{x} = \frac{3 {}^{2} }{3 {}^{x} } \\ \\ we \: know = > \frac{x {}^{a} }{x {}^{b} } = x {}^{a - b} \\ \\ 27 {}^{x} = 3 {}^{2 - x} \\ \\ 3 {}^{3x} = 3 {}^{2 - x} \\ \\ we \: know = > \: \:when \: \: x {}^{a} = x {}^{b} = > a = b \\ \\ then > \\ \\ 3x = 2 - x \\ \\ 4x = 2 \\ \\ x = \frac{2}{4} \\ \\ x = \frac{1}{2}$

hope it helps u...

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