I have this question for Discrete Math. We are currently on Simple Interest, but I have no idea how to solve this.:

Given that u and v are real numbers and that 3^u=10 and 3^v=(1/2) check all the answers that are true statements.
(3^u means 3 raised to the u power).

3^(uv)=5
3^(v+2)=18
3^(u+v)=5
3^(2-v)=18

Question

I have this question for Discrete Math. We are currently on Simple Interest, but I have no idea how to solve this.:

Given that u and v are real numbers and that 3^u=10 and 3^v=(1/2) check all the answers that are true statements.
(3^u means 3 raised to the u power).

3^(uv)=5		
3^(v+2)=18		
3^(u+v)=5		
3^(2-v)=18

anonymous · Answer

$$3^{v+2}=3^v\times 3^2=\frac{1}{2}\times 9$$ so not that one

anonymous · Answer

$$3^{u+v}=3^u\times 3^v=10\times \frac{1}{2}=5$$  so that looks good

anonymous · Answer

$$3^{2-v}=3^2\times 3^{-v}=9\times \frac{1}{3^v}=9\times 2=18$$

anonymous · Answer

Here are some identities you need to solve your question:
$$a^{vu} = (a^{v})^{u}$$$$a^{u+v} = a^{u} \times a^{v}$$

mateeldaa · Answer

Thanks!! I'm not sure how to give you both medals for your help. :\

anonymous · Answer

don't worry about it lol.