QuestionFind $f(\ln 3)$ for the function $f(x)=2 e^{2 x}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)= e^{ x}$ . The value of x is $\ln3$

STEP 2

We need to find the value of the function $f(x)$ at $x=\ln$ . We can do this by substituting $x=\ln$ into the function.
$f(x) =2 e^{2 x}$

STEP 3

Substitute $x=\ln3$ into the function.
$f(\ln3) =2 e^{2 \ln3}$

STEP 4

We can simplify $2 \ln3$ to $\ln3^2$ because of the logarithm property $\ln a^b = b \ln a$ .
$f(\ln3) =2 e^{\ln3^2}$

STEP 5

We know that $e^{\ln a} = a$ , so we can simplify $e^{\ln3^2}$ to $3^2$ .
$f(\ln3) =2 \cdot3^2$

STEP 6

Calculate the value of the function at $x=\ln3$ .
$f(\ln3) =2 \cdot3^2 =18$ So, the value of the function $f(x)=2 e^{2 x}$ at $x=\ln3$ is18.

Was this helpful?

QuestionFind $f(\ln 3)$ for the function $f(x)=2 e^{2 x}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)= e^{ x}$ . The value of x is $\ln3$

STEP 2

We need to find the value of the function $f(x)$ at $x=\ln$ . We can do this by substituting $x=\ln$ into the function.
$f(x) =2 e^{2 x}$

STEP 3

Substitute $x=\ln3$ into the function.
$f(\ln3) =2 e^{2 \ln3}$

STEP 4

We can simplify $2 \ln3$ to $\ln3^2$ because of the logarithm property $\ln a^b = b \ln a$ .
$f(\ln3) =2 e^{\ln3^2}$

STEP 5

We know that $e^{\ln a} = a$ , so we can simplify $e^{\ln3^2}$ to $3^2$ .
$f(\ln3) =2 \cdot3^2$

STEP 6

Calculate the value of the function at $x=\ln3$ .
$f(\ln3) =2 \cdot3^2 =18$ So, the value of the function $f(x)=2 e^{2 x}$ at $x=\ln3$ is18.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionFind f(ln⁡3)f(\ln 3)f(ln3) for the function f(x)=2e2xf(x)=2 e^{2 x}f(x)=2e2x.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=exf(x)= e^{ x}f(x)=ex . The value of x is ln⁡3\ln3ln3

STEP 2

We need to find the value of the function f(x)f(x)f(x) at x=ln⁡x=\lnx=ln. We can do this by substituting x=ln⁡x=\lnx=ln into the function.f(x)=2e2xf(x) =2 e^{2 x}f(x)=2e2x

STEP 3

Substitute x=ln⁡3x=\ln3x=ln3 into the function.f(ln⁡3)=2e2ln⁡3f(\ln3) =2 e^{2 \ln3}f(ln3)=2e2ln3

STEP 4

We can simplify 2ln⁡32 \ln32ln3 to ln⁡32\ln3^2ln32 because of the logarithm property ln⁡ab=bln⁡a\ln a^b = b \ln alnab=blna.f(ln⁡3)=2eln⁡32f(\ln3) =2 e^{\ln3^2}f(ln3)=2eln32

STEP 5

We know that eln⁡a=ae^{\ln a} = aelna=a, so we can simplify eln⁡32e^{\ln3^2}eln32 to 323^232.f(ln⁡3)=2⋅32f(\ln3) =2 \cdot3^2f(ln3)=2⋅32

STEP 6

Calculate the value of the function at x=ln⁡3x=\ln3x=ln3.f(ln⁡3)=2⋅32=18f(\ln3) =2 \cdot3^2 =18f(ln3)=2⋅32=18So, the value of the function f(x)=2e2xf(x)=2 e^{2 x}f(x)=2e2x at x=ln⁡3x=\ln3x=ln3 is18.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionFind $f(\ln 3)$ for the function $f(x)=2 e^{2 x}$ .

Assumptions1. The function is $f(x)= e^{ x}$ . The value of x is $\ln3$

We need to find the value of the function $f(x)$ at $x=\ln$ . We can do this by substituting $x=\ln$ into the function.
$f(x) =2 e^{2 x}$

Substitute $x=\ln3$ into the function.
$f(\ln3) =2 e^{2 \ln3}$

We can simplify $2 \ln3$ to $\ln3^2$ because of the logarithm property $\ln a^b = b \ln a$ .
$f(\ln3) =2 e^{\ln3^2}$

We know that $e^{\ln a} = a$ , so we can simplify $e^{\ln3^2}$ to $3^2$ .
$f(\ln3) =2 \cdot3^2$

Calculate the value of the function at $x=\ln3$ .
$f(\ln3) =2 \cdot3^2 =18$ So, the value of the function $f(x)=2 e^{2 x}$ at $x=\ln3$ is18.