Question

Find f(5) for f(x)=1/9(3)^x

Answer 1

We know: 9 = 3²

Therefore $\dfrac{1}{9}=\dfrac{1}{3^2}$

We know the property:

$\dfrac{a^n}{a^m}=a^{n-m}$

Therefore $\dfrac{1}{9}\cdot3^x=\dfrac{3^x}{3^2}=3^{x-2}$

We must find f(5). Put x = 5 to the equation of the function:

$f(5)=3^{5-2}=3^3=3\cdot3\cdot3=27$

Answer: f(5) = 27.