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Solve the logarithmic equation $\log \left(x-1\right)-\log \left(x+3\right)=-\log \left(x\right)$

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 Final answer to the problem

$x=3$
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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
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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log \left(\frac{x-1}{x+3}\right)=-\log \left(x\right)$

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

$\log \left(\frac{x-1}{x+3}\right)=-\log \left(x\right)$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log(x+-1)-log(x+3)=-log(x). 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). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=-1 and b=10. 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. Multiply both sides of the equation by x+3.

 Final answer to the problem

$x=3$

 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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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

 Main Topic: Logarithmic Equations

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