Question

Trebuie schimbate bazele?

Answer 1

log(2)8*√2=log(2)2³*2^(1/2)=log(2)2^(3+1/2)=log(2)2^7/2=7/2
log(3)3*√3=log(3)3*3^(1/2)=log(3)3^(1+1/2)=log(3)3^3/2=3/2
7/2-3/2=4/2=2

Answer 2

$\log_{\big2}8\sqrt2-\log_{\big3}3\sqrt3= \\ \\ = \log_{\big2}8+\log_{\big2}\sqrt2- \big(\log_{\big3}3+\log_{\big3} \sqrt3\big) = \\ \\ = 3+\log_{\big2}2^{\dfrac{1}{2}}-\Big(1+\log_{\big3}3^{\dfrac{1}{2}}\Big) = \\ \\ = 3+\dfrac{1}{2}\cdot \log_{\big2}2-\Big(1+\dfrac{1}{2}\cdot \log_{\big3}3\Big) = \\ \\ = 3+\dfrac{1}{2}-\Big(1+\dfrac{1}{2}\Big) = \\ \\ = \dfrac{7}{2} - \dfrac{3}{2}} = \\ \\ = \dfrac{4}{2} = \\ \\ =2$