Question

Please help me solve the problems

Answer 1

Answer: Second Option

`x = 2`

Explanation:

We know that:

`f(x) =2(3)^x`

We also know that

`g (x) =3^x +9`

We are looking to solve the following equation

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

Note that this is the same as:

`f(x) =g(x)`

In summary we are looking for a value of x for which it is true that
`f(x) =g(x)`

Then look in the tables shown in the image for a value of x for which it is true that
`f(x) =g(x)`

Note that when
`x = 2` then
`f(x) = 18` and when
`x = 2` then
`g(x) = 18`.

Therefore when
`x = 2` then
`f(x) =g(x)`

The solution of the equation is
`x = 2`

Answer 2

Option B (x = 2).

Explanation:

In this question, two functions are given. The values of input (x) and values of output (f(x) and g(x)) are given. It is given that:

f(x) = 2*3^x

g(x) = 3^x + 9.

The question states what is the value of x if f(x) = g(x) according to the table. The condition actually means that there exists a value of x at which both the functional values are same. From the table, the value of x has to be seen given that f(x) = g(x) i.e. 2*3^x = 3^x + 9. It can be seen at f(x) = 18 and g(x) = 18, the input value is the same i.e. x = 2. This means that x = 2 is the solution of the equation. It can be verified by plugging in the value x = 2 in the equation (18 = 18). Therefore, Option B is the correct choice!!!