Harison ,
a) [tex3]\log_{22}3[/tex3]
[tex3]=\frac{\log_63}{\log_622}[/tex3]
[tex3]=\frac{\log_6(\frac{6}{2})}{\log_6(2.11)}[/tex3]
[tex3]=\frac{\log_66-\log_62}{\log_62+\log_611}[/tex3]
[tex3]=\frac{1-0,37}{0,37+1,34}[/tex3]
[tex3]{\color{red}\boxed{≈0,37}}[/tex3]
b) [tex3]\log_6(4.\sqrt{11})[/tex3]
[tex3]=\log_64+\log_6\sqrt{11}[/tex3]
[tex3]=\log_62^2+\log_611^{\frac{1}{2}}[/tex3]
[tex3]=2.\log_62+\frac{1}{2}.\log_611[/tex3]
[tex3]=2.(0,37)+\frac{1}{2}.(1,34)[/tex3]
[tex3]{\color{red}\boxed{=1,41}}[/tex3]
c) [tex3]\log_{\sqrt{2}}22[/tex3]
[tex3]=\log_{2^{\frac{1}{2}}}22[/tex3]
[tex3]=2.\log_222[/tex3]
[tex3]=2.\left(\frac{\log_622}{\log_62}\right)[/tex3]
[tex3]=2.\left(\frac{\log_6(2.11)}{\log_62}\right)[/tex3]
[tex3]=2.\left(\frac{\log_62+\log_611}{\log_62}\right)[/tex3]
[tex3]=2.\left(\frac{0,37+1,34}{0,37}\right)[/tex3]
[tex3]{\color{red}\boxed{≈9,24}}[/tex3]
