Question

Find a equivalent function to f(x)=4(7)^2x

a. f(x)=28^2x
b. f(x)=4(49)^x
c. f(x)=196^X
d. f(x)=16^x(49)^x

Answer 1

`f(x)=4(7)^(2x)`

Let's look at the way each of these attempts to simplify our expression.

Answer A simply mulltiplies the 4 and the 7 to get 28. This is the correct answer.

The reason you can't just do squaring (to the power of 2) and then go to the power of x later is because you would write that as
`n^(2^x)`, not
`n^(2x)`.

Answer 2

Option: B is correct. (
`f(x)=4* (49)^x`)

Explanation:

We are asked to find which expression is equivalent to the mathematical expression:

`f(x)=4(7)^(2x)`

We know that any expression of the kind
`a^(mn)` could also be represented as
`(a^m)^n`

Hence on converting the given expression using the above representation we have:

`f(x)=4* (7)^(2x)=4* (7^2)^x=4* (49)^x`

Hence f(x) could also be written as:

`f(x)=4* (49)^x`

Hence, option B is correct.