Question

What is value of log 2√2 to the base √2

Answer 1

Answer:

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