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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

don't worry about it lol.