Solve the logarithmic equation $\ln\left(-x\right)=\ln\left(x^2-6\right)$

Step-by-step Solution

Go!
Symbolic mode
Text mode
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

Final answer to the problem

$x=-3$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
  • Load more...
Can't find a method? Tell us so we can add it.
1

For two logarithms of the same base to be equal, their arguments must be equal. In other words, if $\ln(a)=\ln(b)$ then $a$ must equal $b$

$-x=x^2-6$

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

$-x=x^2-6$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation ln(-x)=ln(x^2-6). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \ln(a)=\ln(b) then a must equal b. Multiply both sides of the equation by -1. Move everything to the left hand side of the equation. Sort the polynomial x+x^2-6 in descending order to handle it more easily.

Final answer to the problem

$x=-3$

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

Help us improve with your feedback!

Function Plot

Plotting: $\ln\left(-x\right)-\ln\left(x^2-6\right)$

SnapXam A2
Answer Assistant

beta
Got a different 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

How to improve your answer:

Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

15 min of tutoring / month with Felipe, creator of SnapXam.

Premium access on our iOS and Android apps.

20% discount on online tutoring with us.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account