Question

For which the value of f(x) = 2x^2 + 9 will be the same as g(x) = 3^x?

Answer 1

For
`x = 3` the value of
`f(x) = 2\cdot x^(2)+9` will be the same of
`g(x) = 3^(x)`.

Explanation:

To determine for which value of
`x`, we need to apply the following identity (
`f(x) = g(x)`) and solve numerically the resulting expression:

`2\cdot x^(2)+9 = 3^(x)`

`3^(x)-2\cdot x^(2)-9=0` (1)

A quick approach is using graphic tool and looking for the value of
`x` such that
`3^(x)-2\cdot x^(2)-9=0`. The result of the analysis is included below in the attached image. We find the following result:

`x = 3`

For
`x = 3` the value of
`f(x) = 2\cdot x^(2)+9` will be the same of
`g(x) = 3^(x)`.