Question

I need help with this question

Answer 1

`\text{log}_a(1.5^(-1))=(-9)/(5)`

Explanation:

Given;

`\text{log}_a(2)=(1)/(2)`

`\text{log}_a(3)=5`

By using logarithmic properties,

`\text{log}_a(2)-\text{log}_a(3)=(1)/(2)-5`

`\text{log}_a((2)/(3))=(1)/(2)-5`

`\text{log}_a((1)/((3)/(2)))=(1)/(2)-5`

`\text{log}_a((1)/(1.5))=(1)/(2)-5`

`\text{log}_a(1.5^(-1))=(1-10)/(5)`

`\text{log}_a(1.5^(-1))=(-9)/(5)`