Solve the logarithmic equation $2\log \left(3x-2\right)-1=\log \left(x+6\right)$

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

$x=4$
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

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-1$ from both sides of the equation

$2\log \left(3x-2\right)-1+1=\log \left(x+6\right)+1$

Learn how to solve problems step by step online.

$2\log \left(3x-2\right)-1+1=\log \left(x+6\right)+1$

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

Create a free account and unlock a glimpse of this solution

Learn how to solve problems step by step online. Solve the logarithmic equation 2log(3*x+-2)-1=log(x+6). We need to isolate the dependent variable x, we can do that by simultaneously subtracting -1 from both sides of the equation. Canceling terms on both sides. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right). Express the numbers in the equation as logarithms of base 10.

Final answer to the problem

$x=4$

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: $2\log \left(3x-2\right)-1-\log \left(x+6\right)$

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:

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