←Vrati se na zadatke2. ZadatakAko je log23=a\log_2 3=alog23=a i log72=b\log_7 2=blog72=b, koliko je log628\log_6 28log628?Rješenjelog628=log228log26=log2(4⋅7)log2(2⋅3)=log24+log27log22+log23=2+1log721+log23=2+1b1+a=2b+1b+ab.\begin{aligned} \log_6 28 &=\frac{\log_2 28}{\log_2 6}\\ &=\frac{\log_2(4\cdot7)}{\log_2(2\cdot3)} =\frac{\log_2 4+\log_2 7}{\log_2 2+\log_2 3}\\ &=\frac{2+\frac{1}{\log_7 2}}{1+\log_2 3}\\ &=\frac{2+\frac1b}{1+a} =\frac{2b+1}{b+ab}. \end{aligned}log628=log26log228=log2(2⋅3)log2(4⋅7)=log22+log23log24+log27=1+log232+log721=1+a2+b1=b+ab2b+1.
