Question

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 :)

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

where did the 1 and 2 come from?

Answer 6

how did you get to \[3=(3/2)^n\]