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Solve the logarithmic equation $y=x\ln\left(x^2\right)$

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Solution

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Final answer to the problem

$y=2x\ln\left(x\right)$
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Step-by-step Solution

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  • Differential
  • Find the derivative
  • Find the integral
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
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1

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$y=2x\ln\left(x\right)$

Final answer to the problem

$y=2x\ln\left(x\right)$

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Function Plot

Plotting: $y-x\ln\left(x^2\right)$

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1
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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

$derivdef\left(\ln\left(x\right)\right)$

Main Topic: Properties of Logarithms

They are properties that can help us simplify expressions with logarithms.

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