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7 Aug 2009 20:53:32 IST

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Find the Log of 1/256 to the base 2.(root 2)

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Find the Log of 1/256 to the base 2.(root 2)

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®µD®A

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7 Aug 2009 20:55:13 IST

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$\log_{2\sqrt2}\frac1{256}$ ??

Tanveer Sarma

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7 Aug 2009 21:18:27 IST

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log (1/256) / log2^3/2 ( Since log_ba = log a / log b )

=log 2^-8 / (3/2 log2)

= -8 * 2/3 * log2/ log2

=-16/3

®µD®A

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7 Aug 2009 21:28:52 IST

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$\log_{2\sqrt2}\frac1{256}\\\\=\log_{2\sqrt2}2\sqrt2^{-\frac{16}{3}}=\frac{-16}{3}$

$2^3=(2\sqrt2)^2\\\\\Rightarrow 2^8=256=(2\sqrt2)^\frac{16}{3}$

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