Step-by-step Solution

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

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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

1

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.

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

Unlock this full step-by-step solution!

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

$x=9$
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1
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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

Time to solve it:

~ 0.09 s