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Simplify logbase2 (8/sq rt 32).

 Dec 15, 2019
 #1
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+1

Simplify logbase2 (8/sq rt 32).

 

Log(2, 8 / (4 * sqrt(2))

 

log(2,  2/sqrt(2))

 

Log(2, sqrt(2))

 

Log(sqrt(2)) / log(2)

 

= 1 / 2

 Dec 15, 2019
 #2
avatar+109518 
+1

Thanks guest.

 

Here is another attack method:

 

\(log_2\;\frac{8}{\sqrt{32}}\\~\\ =log_2\;\frac{2^3}{({2^5})^{0.5}}\\~\\ =log_2\;\frac{2^3}{2^{2.5}}\\~\\ =log_2\;(2^{3-2.5})\\~\\ =log_2\;(2^{0.5})\\~\\ =0.5\;log_2\;(2)\\~\\ =0.5\;*1\\~\\ =0.5\)

.
 Dec 16, 2019

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