Condense the logarithmic expression $\ln\left(x\right)+4\ln\left(y\right)$

Step-by-step Solution

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asin
acos
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sinh
cosh
tanh
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sech
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asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\ln\left(xy^4\right)$
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Step-by-step Solution

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  • Choose an option
  • Condense the logarithm
  • Expand the logarithm
  • Simplify
  • Find the integral
  • Find the derivative
  • Write as single logarithm
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Can't find a method? Tell us so we can add it.
1

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $4$

$\ln\left(x\right)+\ln\left(y^4\right)$
2

Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$

$\ln\left(xy^4\right)$

Final answer to the problem

$\ln\left(xy^4\right)$

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Function Plot

Plotting: $\ln\left(xy^4\right)$

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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: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

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