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Algebra Baldor
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Expand the logarithmic expression $\ln\left(\frac{5x\sqrt{2-7x}}{3\left(x-4\right)^8}\right)$

Step-by-step Solution

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Solution

Final answer to the problem

$\ln\left(x\right)+\frac{1}{2}\ln\left(2-7x\right)+\ln\left(5\right)-\ln\left(3\right)-8\ln\left(x-4\right)$
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Step-by-step Solution

How should I solve this problem?

  • 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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1

The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator

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$\ln\left(5x\sqrt{2-7x}\right)-\ln\left(3\left(x-4\right)^8\right)$

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Learn how to solve problems step by step online. Expand the logarithmic expression ln((5x(2-7x)^(1/2))/(3(x-4)^8)). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right).

Final answer to the problem

$\ln\left(x\right)+\frac{1}{2}\ln\left(2-7x\right)+\ln\left(5\right)-\ln\left(3\right)-8\ln\left(x-4\right)$

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Function Plot

Plotting: $\ln\left(x\right)+\frac{1}{2}\ln\left(2-7x\right)+\ln\left(5\right)-\ln\left(3\right)-8\ln\left(x-4\right)$

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0
a
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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

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