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Condense the logarithmic expression $2\ln\left(x+1\right)-\ln\left(x\right)$

Step-by-step Solution

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asinh
acosh
atanh
acoth
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Final answer to the problem

$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$
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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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1

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $2$

$\ln\left(\left(x+1\right)^2\right)-\ln\left(x\right)$
2

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

$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$

Final answer to the problem

$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$

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Function Plot

Plotting: $\ln\left(\frac{\left(x+1\right)^2}{x}\right)$

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1
2
3
4
5
6
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: 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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