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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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###  Videos

$\ln\left(\frac{\left(x+1\right)^2}{x}\right)$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

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: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

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

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite as single logarithmCondense the logarithmExpand the logarithmSolve for x

SnapXam A2

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a
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

### Main topic:

Condensing Logarithms

~ 0.03 s

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