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hello can u give me some tips how to easily calculate for example x=log(1/16)2 i know its (1/16)^x = 2 but i dont know how to calculate that x

 Aug 7, 2016
 #1
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hello can u give me some tips how to easily calculate for example x=log(1/16)2 i know its (1/16)^x = 2 but i dont know how to calculate that x

 

\(x=log_{(1/16)}2\\ \left(\frac{1}{16}\right)^x=2\\ \left(\frac{1}{2^4}\right)^x=2\\ \left(2^{-4}\right)^x=2^1\\ 2^{-4x}=2^1\\ -4x=1\\ x=\frac{-1}{4}\\~\\ or\\ x=log_{(1/16)}2\\ \left(\frac{1}{16}\right)^x=2\\ log_{10}\left(\frac{1}{16}\right)^x=log_{10}2\\ xlog_{10}\left(\frac{1}{16}\right)=log_{10}2\\ x=log_{10}2 \div log_{10}\left(\frac{1}{16}\right)\\ \)

 

(log(2)/-1.2041199826559248) = -0.25

 Aug 7, 2016
 #2
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+5

ty very much melody

 Aug 8, 2016

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