Question Find the equivalent function to $f(x)=2(5)^{2x}$ : $f(x)=50^{x}$ , $f(x)=100^{x}$ , $f(x)=2(25)^{x}$ , or $f(x)=4(25)^{x}$ ?

Studdy Solution

STEP 1

Assumptions1. We are given the function $f(x)=(5)^{x}$ . . We are looking for an equivalent function among the given options.

STEP 2

First, let's simplify the given function. We can do this by using the property of exponents that $(a^{b})^{c} = a^{bc}$ .
$f(x)=2(5)^{2x} =2((5^{2})^{x})$

STEP 3

Now, simplify the exponent $5^{2}$ .
$f(x)=2((5^{2})^{x}) =2((25)^{x})$

STEP 4

We can see that the function $f(x)=2((25)^{x})$ is equivalent to the given function $f(x)=2()^{2x}$ .Therefore, the equivalent function is $f(x)=2(25)^{x}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms