## anonymous 5 years ago Can someone solve this please? the points (2,6) and (3,18) lie on the curve y=ax^n use logarithms to find the values of a and n, giving your answers correct to 2d.p. thanks :)

1. anonymous

Substitute the two points in the given equation, gives us the two following equations: $6=a(2)^n \rightarrow(1)$ and$18=a(3)^n \rightarrow(2)$ Now, we should solve the two equations for the two unknowns a and n

2. anonymous

Using the first equation we have: $a={6 \over 2^n}\rightarrow(*)$ Substitute (*) into equation (2): $18={6 \over 2^n}(3)^n \implies 3=({3 \over 2})^n \implies \log(3)=n(\log({3 \over 2}))\implies n={\log(3) \over \log({3 \over 2})}$

3. anonymous

That's n=2.71. Now substitute this value of n into (*) to get a.

4. anonymous

So $a={6 \over 2^n}={6 \over 2^2.71}\approx0.92$

5. anonymous

where did the 1 and 2 come from?

6. anonymous

how did you get to $3=(3/2)^n$