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Solve the logarithmic equation $\log \left(x-1\right)+\log \left(x+1\right)=2\log \left(x+2\right)$

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 Final answer to the problem

$x=\frac{5}{-4}$
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 Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
1

Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$, where $a=2$, $b=10$ and $x=x+2$

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

Learn how to solve logarithmic equations problems step by step online.

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

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log(x+-1)+log(x+1)=2log(x+2). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=2, b=10 and x=x+2. The sum of two logarithms of the same base is equal to the logarithm of the product of the arguments. Solve the product of difference of squares \left(x-1\right)\left(x+1\right). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b.

 Final answer to the problem

$x=\frac{5}{-4}$

 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

SnapXam A2

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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

 Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.