👉 Try now NerdPal! Our new math app on iOS and Android

Expand the logarithmic expression $\frac{1}{2\pi }\ln\left(\frac{10^2}{\frac{16\cdot \left(\frac{4613}{500000}\right)\cdot 9}{4}}\right)+\frac{1}{\pi }\ln\left(\frac{\left(\frac{\left(\frac{3}{4}\right)\cdot 5}{6}\right)\cdot 7}{8}\right)$

Step-by-step Solution

Go!
Math 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

$\frac{53}{333}\ln\left(301.081485\right)+\frac{1}{\pi}\ln\left(\frac{35}{64}\right)$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Multiply $2$ times $\pi $

$\frac{1}{2\pi }\ln\left(\frac{10^2}{\frac{16\cdot \left(\frac{4613}{500000}\right)\cdot 9}{4}}\right)+\frac{1}{\pi }\ln\left(\frac{\left(\frac{\left(\frac{3}{4}\right)\cdot 5}{6}\right)\cdot 7}{8}\right)$

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

$\frac{1}{2\pi }\ln\left(\frac{10^2}{\frac{16\cdot \left(\frac{4613}{500000}\right)\cdot 9}{4}}\right)+\frac{1}{\pi }\ln\left(\frac{\left(\frac{\left(\frac{3}{4}\right)\cdot 5}{6}\right)\cdot 7}{8}\right)$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve expanding logarithms problems step by step online. Expand the logarithmic expression 1/(2*pi)ln((10^2)/((164613/500000*9)/4))+1/piln(((3/45)/67)/8). Multiply 2 times \pi . Multiply 16 times 9. Divide 1 by 2\pi . Divide 4613 by 500000.

Final Answer

$\frac{53}{333}\ln\left(301.081485\right)+\frac{1}{\pi}\ln\left(\frac{35}{64}\right)$

Exact Numeric Answer

$0.7162$

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

SimplifyWrite as single logarithmCondense the logarithmFind the integralFind the derivative

Give us your feedback!

Function Plot

Plotting: $\frac{53}{333}\ln\left(301.081485\right)+\frac{1}{\pi}\ln\left(\frac{35}{64}\right)$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Main Topic: Expanding Logarithms

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

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account