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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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Final Answer

$x=9$
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Step-by-step Solution

Problem to solve:

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

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.

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

Unlock the first 3 steps of this solution!

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.

Final Answer

$x=9$
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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

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:

Logarithmic Equations

Time to solve it:

~ 0.05 s