Oblicz: a)   [latex]2 ^{ log_{4}25[/latex] b)log15+log50-log[latex] frac{3}{4} [/latex] [latex] log_{3}25* log_{5}27[/latex] prosze

[latex]a);log_425=frac{log_225}{log_24}=frac{log_225}{2}\2^{log_425}=2^{frac{log_225}{2}}=(2^{log_225})^frac12=...\(log_225=log_225Leftrightarrow 2^{log_225}=25)\...=25^{frac12}=sqrt{25}=5\\b);log15+log50-logfrac34=log(15cdot50cdotfrac43)=\=log(1000)=3\\c);log_325cdotlog_527=frac{log_525}{log_53}cdotfrac{log_327}{log_35}=...\(log_ab=frac1{log_ba})\...=frac{2cdot3cdotlog_35}{log_35}=6[/latex]