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

# Condense the logarithmic expression $3\ln\left(a\right)-\frac{1}{2}\left(\ln\left(b\right)+\ln\left(c^2\right)\right)$

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

$\ln\left(\frac{a^3}{\sqrt{b}c}\right)$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
• FOIL Method
Can't find a method? Tell us so we can add it.
1

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $3$

$\ln\left(a^3\right)-\frac{1}{2}\left(\ln\left(b\right)+\ln\left(c^2\right)\right)$

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

$\ln\left(a^3\right)-\frac{1}{2}\left(\ln\left(b\right)+\ln\left(c^2\right)\right)$

Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression 3ln(a)-1/2(ln(b)+ln(c^2)). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals 3. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n). The power of a product is equal to the product of it's factors raised to the same power.

##  Final answer to the problem

$\ln\left(\frac{a^3}{\sqrt{b}c}\right)$

##  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: Condensing Logarithms

Combining or condensing logarithms consists of rewriting a mathematical expression with several logarithms into a single logarithm, by applying the properties of logarithms.