Answer:
[tex]\text{log}_a(1.5^{-1})=\frac{-9}{5}[/tex]
Step-by-step explanation:
Given;
[tex]\text{log}_a(2)=\frac{1}{2}[/tex]
[tex]\text{log}_a(3)=5[/tex]
By using logarithmic properties,
[tex]\text{log}_a(2)-\text{log}_a(3)=\frac{1}{2}-5[/tex]
[tex]\text{log}_a(\frac{2}{3})=\frac{1}{2}-5[/tex]
[tex]\text{log}_a(\frac{1}{\frac{3}{2}})=\frac{1}{2}-5[/tex]
[tex]\text{log}_a(\frac{1}{1.5})=\frac{1}{2}-5[/tex]
[tex]\text{log}_a(1.5^{-1})=\frac{1-10}{5}[/tex]
[tex]\text{log}_a(1.5^{-1})=\frac{-9}{5}[/tex]
