Condense the logarithmic expression $2\log \left(x+3\right)+3\log \left(x-7\right)-5\log \left(x-2\right)+2\log \left(x\right)$

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Final answer to the problem

$\log \left(\frac{\left(x+3\right)^2\left(x-7\right)^3x^2}{\left(x-2\right)^{5}}\right)$
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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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Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$

$\log \left(\left(x+3\right)^2\right)+\log \left(\left(x-7\right)^3\right)-5\log \left(x-2\right)+\log \left(x^2\right)$

Learn how to solve condensing logarithms problems step by step online.

$\log \left(\left(x+3\right)^2\right)+\log \left(\left(x-7\right)^3\right)-5\log \left(x-2\right)+\log \left(x^2\right)$

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Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression 2log(x+3)+3log(x+-7)-5log(x+-2)2log(x). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\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). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n).

Final answer to the problem

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

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Function Plot

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

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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
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: Condensing Logarithms

Combining or condensing logarithms consists of rewriting a mathematical expression with several logarithms into a single logarithm, by applying the properties of logarithms.

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