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# Solve the logarithmic equation $\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$

## Step-by-step Solution

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### Videos

$x=9$
Got another answer? Verify it here!

## Step-by-step Solution

Problem to solve:

$\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$

Specify the solving method

1

Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$

$\ln\left(2x^3\left(\frac{1}{x}\right)\right)=\ln\left(486\right)-\ln\left(3\right)$

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

$\ln\left(2x^3\left(\frac{1}{x}\right)\right)=\ln\left(486\right)-\ln\left(3\right)$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation ln(1/x)+ln(2x^3)=ln(486)-ln(3). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Multiply the fraction and term. Simplify the fraction \frac{2x^3}{x} by x. Take the variable outside of the logarithm.

$x=9$
SnapXam A2

### beta Got another 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

$\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$