a)
[tex]\begin{gathered} \log _a(1.8)= \\ =\log _a(\frac{9}{5})= \\ =\log _a(9)-\log _a(5)= \\ =\log _a(3^2)-\log _a(5)= \\ =2\log _a(3^{})-\log _a(5)= \\ \approx2\cdot0.79-1.16\approx \\ \approx0.42 \end{gathered}[/tex]b)
[tex]\begin{gathered} \log _a(\sqrt[]{5})= \\ =\log _a(5^{\frac{1}{2}})= \\ =\frac{1}{2}\log _a(5)= \\ \approx\frac{1}{2}\cdot1.16\approx0.58 \end{gathered}[/tex]c)
[tex]\begin{gathered} \log _a(15)= \\ =\log _a(3\cdot5)= \\ =\log _a(3)+\log _a(5)= \\ \approx0.79+1.16\approx1.95 \end{gathered}[/tex]d)
[tex]\begin{gathered} \log _a(45)= \\ =\log _a(9\cdot5)= \\ =\log _a(9)+\log _a(5)= \\ =\log _a(3^2)+\log _a(5)= \\ =2\log _a(3^{})+\log _a(5)= \\ \approx2\cdot0.79+1.16\approx2.74 \end{gathered}[/tex]e)
[tex]\begin{gathered} \log _a(0.6)= \\ =\log _a(\frac{3}{5})= \\ =\log _a(3)-\log _a(5)= \\ \approx0.79-1.16\approx-0.37 \end{gathered}[/tex]f)
[tex]\begin{gathered} \log _a(9)= \\ =\log _a(3^2)= \\ =2\log _a(3)= \\ \approx2\cdot0.79\approx1.58 \end{gathered}[/tex]
