How do you evaluate $log_sqrt8 4096$ ?

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Answer 1 · 2016-11-17T03:06:22

$log_(sqrt8)4096=8$

Let $log_(sqrt8)4096=x$

Using definition of logarithm that $log_ab=m$ means $a^m=b$

$(sqrt8)^x=4096$

expressing them in powers of $x$

or $(sqrt2^3)^x=2^12$

or $((2^(1/2))^3)^x=2^12$

or $2^((3x)/2)=2^12$

or $(3x)/2=12$

i.e. $x=12xx2/3=8$

Hence $log_(sqrt8)4096=8$

How do you evaluate log_sqrt8 4096log_sqrt8 4096?