Question

log2 2 radicaldin32​

Answer 1

Explicație pas cu pas:

$log_{2}(2 \sqrt{32} ) = log_{2}(2 \sqrt{16 \times 2} ) = log_{2}(2 \sqrt{4 {}^{2} \times 2 } ) = log_{2}(2 \times 4 \sqrt{2} ) = log_{2}(8 \sqrt{2} ) \\ log_{a}(b \times c) = log_{a}(b) + log_{a}(c) \\ log_{2}(8 \sqrt{2} ) = log_{2}(8) + log_{2}( \sqrt{2} ) = 3 + log_{2}( {2}^{ \frac{1}{2} } ) = 3 + \frac{1}{2} log_{2}(2) = 3 + \frac{1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$