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3 years ago

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What is the value of x in the equation below?

1 answer:

denis23 [38]3 years ago

6 0

Answer:

Step-by-step explanation:

Alright, lets get started.

The given equation is :

$1+2e^{x+1}=9$

Subtracting 1 in both sides

$1+2e^{x+1}-1=9-1$

$2e^{x+1}=8$

Dividing 2 in both sides

$e^{x+1}=\frac{8}{2}$

$e^{x+1}=4$

Taking log on both sides

$loge^{(x+1)}=log4$

$(x+1)loge=log4$

Plugging the value of log e as 1

$x+1=log4$

$x=log4-1$ ..................... Answer

Hope it will help :)

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galina1969 [7]

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3 years ago

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G(x)=-2x-9 what is g(-7)

matrenka [14]

Answer:

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Step-by-step explanation:

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function <em>f</em>, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to <em>x</em> :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to <em>y</em> :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to <em>y</em> :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

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3 years ago

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Ainat [17]

Answer:

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Step-by-step explanation:

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