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Bogdan [553]
3 years ago
11

What is the solution to the equation e^3x=12 Round your answer to the nearest hundredth

Mathematics
2 answers:
ch4aika [34]3 years ago
7 0

Answer:

.83 A

Step-by-step explanation:


Lunna [17]3 years ago
3 0

Keywords:

<em>equation, variable, clear, round, centesima, neperian logarithm, exponential </em>

For this case we have the following equation e ^ {3x} = 12, from which we must clear the value of the variable "x" and round to the nearest hundredth. To do this, we must apply properties of neperian and exponential logarithms. By definition:

ln (e ^ x) = x

So:

e ^ {3x} = 12 We apply Neperian logarithm to both sides:

ln (e^{3x}) = ln (12)\\3x = ln (12)

We divide between "3" both sides of the equation:

\frac {3x} {3} = \frac {ln (12)} {3}\\x = \frac {ln (12)} {3}\\x = 0.828302217

Rounding out the nearest hundredth we have:

x = 0.83

Answer:

x = 0.83

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\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)

where \partial_\xi denotes the partial derivative operator with respect to \xi. Recall that

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The cross product reduces to

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Integrate both sides of

\dfrac{\partial f}{\partial y}=2xze^{2xyz}

with respect to y and

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Differentiate both sides with respect to x and

\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}

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\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}

2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}

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

\implies h(z)=C

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f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C

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