# Step-by-step Solution

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## Final Answer

$x=9$
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## Step-by-step Solution

Problem to solve:

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

Choose the solving method

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The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator

$-\ln\left(x\right)+\ln\left(2x^3\right)=5.087596$

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

$-\ln\left(x\right)+\ln\left(2x^3\right)=5.087596$

Learn how to solve rational equations problems step by step online. Solve the equation ln(1/x)+ln(2x^3)=ln(486)-ln(3). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Simplify the fraction \frac{2x^3}{x} by x. Take the variable outside of the logarithm.

## Final Answer

$x=9$
SnapXam A2
Answer Assistant

Go!
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5
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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

### Tips on how to improve your answer:

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

### Main topic:

Rational equations

~ 0.09 s