Solve the exponential equation $e^{2x}-e^x-6=0$

Step-by-step Solution

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acosh
atanh
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Final answer to the problem

$x=\ln\left(3\right)$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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1

Rewriting the exponent $e^{2x}$

Learn how to solve constant rule for differentiation problems step by step online.

$\left(e^x\right)^2-e^x-6=0$

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Learn how to solve constant rule for differentiation problems step by step online. Solve the exponential equation e^(2x)-e^x+-6=0. Rewriting the exponent e^{2x}. We can try to factor the expression \left(e^x\right)^2-e^x-6 by applying the following substitution. Substituting in the polynomial, the expression results in. Factor the trinomial u^2-u-6 finding two numbers that multiply to form -6 and added form -1.

Final answer to the problem

$x=\ln\left(3\right)$

Exact Numeric Answer

$x=1.0986123$

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Function Plot

Plotting: $e^{2x}-e^x-6$

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Answer Assistant

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Go!
1
2
3
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: Constant Rule for Differentiation

The constant rule for differentiation says that the derivative for any constant $k$ is equal to zero.

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