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Expand the logarithmic expression $\ln\left(\left(x+6\right)^3\left(7x-3\right)^4\right)$

Step-by-step Solution

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Final Answer

$3\ln\left(x+6\right)+4\ln\left(7x-3\right)$
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Step-by-step Solution

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

$\ln\left(\left(x+6\right)^3\right)+\ln\left(\left(7x-3\right)^4\right)$

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$\ln\left(\left(x+6\right)^3\right)+\ln\left(\left(7x-3\right)^4\right)$

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Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression ln((x+6)^3(7x-3)^4). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).

Final Answer

$3\ln\left(x+6\right)+4\ln\left(7x-3\right)$

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SimplifyWrite as single logarithmCondense the logarithmExpand the logarithmFind the integralFind the derivativeSolve for x

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Plotting: $3\ln\left(x+6\right)+4\ln\left(7x-3\right)$

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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: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.

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