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# Solve the logarithmic equation $\log_{3}\left(x+4\right)+\log_{3}\left(x-4\right)=2$

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##  Final answer to the problem

$x=5$
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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

Express the numbers in the equation as logarithms of base $3$

$\log_{3}\left(x+4\right)+\log_{3}\left(x-4\right)=\log_{3}\left(3^{2}\right)$

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

$\log_{3}\left(x+4\right)+\log_{3}\left(x-4\right)=\log_{3}\left(3^{2}\right)$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log3(x+4)+log3(x+-4)=2. Express the numbers in the equation as logarithms of base 3. 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+4\right)\left(x-4\right). Use the following rule for logarithms: \log_b(b^k)=k.

##  Final answer to the problem

$x=5$

##  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.