Expand the logarithmic expression $\log \left(\frac{100x^5\sqrt[3]{2-x}}{7\left(x+4\right)^2}\right)$

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Final answer to the problem

$5\log \left(x\right)+\frac{1}{3}\log \left(2-x\right)+2-2\log \left(x+4\right)-\log \left(7\right)$
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Step-by-step Solution

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  • Choose an option
  • Solve for x
  • 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
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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

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$\log \left(100x^5\sqrt[3]{2-x}\right)-\log \left(7\left(x+4\right)^2\right)$

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Learn how to solve logarithmic differentiation problems step by step online. Expand the logarithmic expression log((100*x^5*(2+-1*x)^(1/3))/(7*(x+4)^2)). The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x^5 and N=100\sqrt[3]{2-x}. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=\sqrt[3]{2-x} and N=100. Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=\left(x+4\right)^2 and N=7.

Final answer to the problem

$5\log \left(x\right)+\frac{1}{3}\log \left(2-x\right)+2-2\log \left(x+4\right)-\log \left(7\right)$

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Function Plot

Plotting: $5\log \left(x\right)+\frac{1}{3}\log \left(2-x\right)+2-2\log \left(x+4\right)-\log \left(7\right)$

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7
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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: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

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