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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

$x=9$
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##  Step-by-step Solution 

Problem to solve:

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

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1

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

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

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

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

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. 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).

$x=9$

##  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

Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even pointsFind the discriminant

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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:

Logarithmic Equations

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