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Solve the exponential equation $y^{-3}=x^3\left(3e^x+c\right)$

Step-by-step Solution

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Final answer to the problem

$c=\frac{1}{y^{3}x^{3}}-3e^x$
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Step-by-step Solution

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Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{1}{y^{3}}=x^3\left(3e^x+c\right)$

Learn how to solve exponential equations problems step by step online.

$\frac{1}{y^{3}}=x^3\left(3e^x+c\right)$

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Learn how to solve exponential equations problems step by step online. Solve the exponential equation y^(-3)=x^3(3e^x+c). Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Rearrange the equation. Multiply the equation by the reciprocal of x^3. Multiply the fraction and term.

Final answer to the problem

$c=\frac{1}{y^{3}x^{3}}-3e^x$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for ySolve for xSolve for cFind the discriminantFind the derivativeSolve by implicit differentiationSolve for y'Find dy/dxDerivative

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Function Plot

Plotting: $y^{-3}-x^3\left(3e^x+c\right)$

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1
2
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4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Exponential Equations

Exponential equations are those where the unknown appears only in the exponents of powers of constant bases.

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