Pojednostavi:\( \)

\begin{gather*}\mathbf{1)}\:\:\frac{\log225}{log3+\log5};\quad\quad\mathbf{2)}\:\:\frac{2\log2+\log7}{1+\log2.8}\end{gather*}

\(\textbf{Rješenje:}\)

\begin{gather*}\mathbf{1)}\:\:\frac{\log225}{log3+\log5}=\frac{\log15^2}{\log(3\cdot 5)}=\frac{2\log15}{\log15}=2\end{gather*}

\begin{gather*}\mathbf{2)}\:\:\frac{2\log2+\log7}{1+\log2.8}=\frac{\log2^2+\log7}{log10+\log2.8}\\=\frac{\log(2^2\cdot 7)}{\log(10\cdot 2.8)}=\frac{\log28}{\log28}=1\end{gather*}