Question

$2log2\sqrt{2}^{15}$
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Answer 1

Step-by-step explanation:

What is the value of 2^ (log base (2 sqrt(2)) of 15) =?

Let T=2log22√15

Recall that logba≡logcalogcb . We can use this to convert our logarithms to base 2.

∴log22√15=log215log222–√

Recall that logab≡loga+logb , and logbba≡a .

∴log222–√=log22+log22–√=log221+log2212=1+12=32

∴log22√15=log21532=23log215

∴T=223log215

Recall that abc≡(ab)c .

∴T=(2log215)23

Recall that blogba≡a .

∴T=1523≈6.0822