Question

evaluate the following
log2 8√2

Answer 1

Thanks for the question !

It's a concept from logarithms.

$log_{2}(8 \sqrt{2} ) \\ \\ = log_{2}( {2}^{3} \times {2}^{ \frac{1}{2} } ) \\ \\ = log_{2}(2 ^{3 + \frac{1}{2} } ) \\ \\ = log_{2}( {2}^{ \frac{7}{2} } ) \\ \\ = \frac{7}{2} log_{2}(2) \\ \\ = \frac{7}{2}$

Wish it helps :)

Answer 2

Answer-

=Log2 8root2

=log2 2^3.2^1/2 ( 8=2^3 or root2= 2^1/2 )

=log2 2^7/2 ......(base (2) same power ‘ multiply)

=log2^7/2 divide log2 ( logA B = logB/logA)

= 7/2*log2/log2

= 7/2

Hope it helps you :)