Question

$log_{2}( \sqrt{32 \sqrt{32 \sqrt{32....... \infty } } } )$
option are a)4. b)5. c)3. d)6

Answer 1

$x = log_{2}( \sqrt{32 \sqrt{32 \sqrt{32 \sqrt{32 \sqrt{32... \infty } } } } } ) \\ multiply \: both \: sides \: by \: 2 \\ 2x = log_{2}(32 \sqrt{32 \sqrt{32 \sqrt{32.. \infty } } } ) \\ 2x = log_{2}(32) + log_{2}( \sqrt{32 \sqrt{32 \sqrt{32.. \infty } } } ) \\ 2x = 5 + x \\ x = 5$
ans.5