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Algebra Baldor
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Condense the logarithmic expression $\ln\left(\frac{x}{\left(x-3\right)\left(x^2-9\right)}\right)+\ln\left(\frac{x+3}{x}\right)$

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Solution

Final answer to the problem

$\ln\left(\frac{x+3}{\left(x-3\right)\left(x^2-9\right)}\right)$
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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
  • Load more...
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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$

$\ln\left(\frac{x}{\left(x-3\right)\left(x^2-9\right)}\frac{x+3}{x}\right)$

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$\ln\left(\frac{x}{\left(x-3\right)\left(x^2-9\right)}\frac{x+3}{x}\right)$

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Learn how to solve problems step by step online. Condense the logarithmic expression ln(x/((x-3)(x^2-9)))+ln((x+3)/x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Multiplying fractions \frac{x}{\left(x-3\right)\left(x^2-9\right)} \times \frac{x+3}{x}. Simplify the fraction \frac{x\left(x+3\right)}{\left(x-3\right)\left(x^2-9\right)x} by x. Simplify the fraction \frac{x\left(x+3\right)}{\left(x-3\right)\left(x^2-9\right)x} by x.

Final answer to the problem

$\ln\left(\frac{x+3}{\left(x-3\right)\left(x^2-9\right)}\right)$

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Function Plot

Plotting: $\ln\left(\frac{x+3}{\left(x-3\right)\left(x^2-9\right)}\right)$

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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
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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