anonymous
  • anonymous
Solve for . Please round the answer to four decimal places. 2^(4/log[3]x)=1/256 Steps would be appreciated.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[2^{4/\log_{3}x }=1/256\]
anonymous
  • anonymous
First consider the fact that 256 = 2^8. Then\[2^{4/\log_3x}=1/2^8=2^{-8}\]
anonymous
  • anonymous
This statement is true only if the exponents are equal. So,\[\frac{4}{\log_3{x}}=-8\]Rearranging,\[\log_3{x}=-\frac{1}{2}\]By the definition of logarithm, this is equivalent to,\[x=3^{-1/2}=\frac{1}{\sqrt{3}}\]

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anonymous
  • anonymous
Thanks a bunches!

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