8-x-x-x-2-Show-that-x-4-

Question Number 7655 by Tawakalitu. last updated on 07/Sep/16

{(\frac{8}{x})}^{x} = x^{2}

S h o w t h a t x = 4

Commented by FilupSmith last updated on 07/Sep/16

trial and error

x = 3

{(\frac{8}{3})}^{3} = 3^{2}

{(2 . \bar{6})}^{3} \neq 9 (2 . \bar{6} = 2 + 0 . \bar{6} \to 2^{3} = 8,

n = 0 . \bar{6}, f o r n > 1, \frac{1}{n^{k}} < 0 \Rightarrow∴ 2 . \bar{6} \neq 9)

{(\frac{8}{4})}^{4} = 4^{2}

2^{4} = 4^{2}

Answered by FilupSmith last updated on 08/Sep/16

{(\frac{8}{x})}^{x} = x^{2}

2^{x} = x^{2}

\frac{8}{x} = 2

8 = 2 x

x = 4

Commented by Tawakalitu. last updated on 09/Sep/16

T h a n k s

Answered by FilupSmith last updated on 08/Sep/16

{(\frac{8}{x})}^{x} = x^{2}

x \ln (\frac{8}{x}) = 2 \ln (x)

\ln (8) - \ln (x) = \frac{2}{x} \ln (x)

\ln (8) = (\frac{2}{x} + 1) \ln (x)

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

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

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

\frac{3}{2} \ln (4) = (\frac{2}{x} + 1) \ln (x)

x = 4 \Rightarrow \frac{2}{4} + 1 = \frac{3}{2}

L H S = R H S

Commented by Tawakalitu. last updated on 09/Sep/16

T h a n k y o u s i r