ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Expand the logarithmic expression $\log_{3}\left(4x\right)$

Go!
Symbolic mode
Text mode
Go!
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

##  Final answer to the problem

$\log_{3}\left(x\right)+2\log_{3}\left(2\right)$
Got another answer? Verify it here!

##  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
Can't find a method? Tell us so we can add it.
1

Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=x$ and $N=4$

$\log_{3}\left(x\right)+\log_{3}\left(4\right)$

Learn how to solve expanding logarithms problems step by step online.

$\log_{3}\left(x\right)+\log_{3}\left(4\right)$

Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression log3(4*x). Use the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right), where M=x and N=4. Decompose 4 in it's prime factors. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).

##  Final answer to the problem

$\log_{3}\left(x\right)+2\log_{3}\left(2\right)$

##  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

SnapXam A2

Go!
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

###  Main Topic: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.