QuestionFind the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

Studdy Solution

STEP 1

Assumptions1. We are looking for the value of x that makes the function equal to zero. . The function is given by $f(x)=()^{x}-16$

STEP 2

We need to set the function equal to zero and solve for x.
$2(2)^{x}-16 =0$

STEP 3

We can start by adding16 to both sides of the equation to isolate the exponential term on one side.
$2(2)^{x} =16$

STEP 4

Next, we divide both sides of the equation by2 to further isolate the exponential term.
$(2)^{x} =8$

STEP 5

We can rewrite8 as a power of2, since8 is a power of2.
$(2)^{x} = (2)^{3}$

STEP 6

Since the bases are equal, the exponents must also be equal. Therefore, we can set the exponents equal to each other and solve for x.
$x =3$ So, the zero of the function is3.

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QuestionFind the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

Studdy Solution

STEP 1

Assumptions1. We are looking for the value of x that makes the function equal to zero. . The function is given by $f(x)=()^{x}-16$

STEP 2

We need to set the function equal to zero and solve for x.
$2(2)^{x}-16 =0$

STEP 3

We can start by adding16 to both sides of the equation to isolate the exponential term on one side.
$2(2)^{x} =16$

STEP 4

Next, we divide both sides of the equation by2 to further isolate the exponential term.
$(2)^{x} =8$

STEP 5

We can rewrite8 as a power of2, since8 is a power of2.
$(2)^{x} = (2)^{3}$

STEP 6

Since the bases are equal, the exponents must also be equal. Therefore, we can set the exponents equal to each other and solve for x.
$x =3$ So, the zero of the function is3.

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QuestionFind the zero of the function f(x)=2(2)x−16f(x)=2(2)^{x}-16f(x)=2(2)x−16. Enter a number.

Studdy Solution

STEP 1

Assumptions1. We are looking for the value of x that makes the function equal to zero. . The function is given by f(x)=()x−16f(x)=()^{x}-16f(x)=()x−16

STEP 2

We need to set the function equal to zero and solve for x.2(2)x−16=02(2)^{x}-16 =02(2)x−16=0

STEP 3

We can start by adding16 to both sides of the equation to isolate the exponential term on one side.2(2)x=162(2)^{x} =162(2)x=16

STEP 4

Next, we divide both sides of the equation by2 to further isolate the exponential term.(2)x=8(2)^{x} =8(2)x=8

STEP 5

We can rewrite8 as a power of2, since8 is a power of2.(2)x=(2)3(2)^{x} = (2)^{3}(2)x=(2)3

STEP 6

Since the bases are equal, the exponents must also be equal. Therefore, we can set the exponents equal to each other and solve for x.x=3x =3x=3So, the zero of the function is3.

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

QuestionFind the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

Assumptions1. We are looking for the value of x that makes the function equal to zero. . The function is given by $f(x)=()^{x}-16$

We need to set the function equal to zero and solve for x.
$2(2)^{x}-16 =0$

We can start by adding16 to both sides of the equation to isolate the exponential term on one side.
$2(2)^{x} =16$

Next, we divide both sides of the equation by2 to further isolate the exponential term.
$(2)^{x} =8$

We can rewrite8 as a power of2, since8 is a power of2.
$(2)^{x} = (2)^{3}$

Since the bases are equal, the exponents must also be equal. Therefore, we can set the exponents equal to each other and solve for x.
$x =3$ So, the zero of the function is3.