Ln(3x+1)=ln(2x-6)

Simple and best practice solution for Ln(3x+1)=ln(2x-6) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for Ln(3x+1)=ln(2x-6) equation: 


Simplifying
Ln(3x + 1) = ln(2x + -6)

Reorder the terms:
nL(1 + 3x) = ln(2x + -6)
(1 * nL + 3x * nL) = ln(2x + -6)
(1nL + 3nxL) = ln(2x + -6)

Reorder the terms:
1nL + 3nxL = ln(-6 + 2x)
1nL + 3nxL = (-6 * ln + 2x * ln)
1nL + 3nxL = (-6ln + 2lnx)

Solving
1nL + 3nxL = -6ln + 2lnx

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '6ln' to each side of the equation.
1nL + 6ln + 3nxL = -6ln + 6ln + 2lnx

Reorder the terms:
6ln + 1nL + 3nxL = -6ln + 6ln + 2lnx

Combine like terms: -6ln + 6ln = 0
6ln + 1nL + 3nxL = 0 + 2lnx
6ln + 1nL + 3nxL = 2lnx

Add '-2lnx' to each side of the equation.
6ln + 1nL + -2lnx + 3nxL = 2lnx + -2lnx

Reorder the terms:
6ln + -2lnx + 1nL + 3nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
6ln + -2lnx + 1nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(6l + -2lx + L + 3xL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0

Subproblem 2
Set the factor '(6l + -2lx + L + 3xL)' equal to zero and attempt to solve:

Simplifying
6l + -2lx + L + 3xL = 0

Reorder the terms:
L + 6l + -2lx + 3xL = 0

Solving
L + 6l + -2lx + 3xL = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1L' to each side of the equation.
L + 6l + -2lx + -1L + 3xL = 0 + -1L

Reorder the terms:
L + -1L + 6l + -2lx + 3xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + 6l + -2lx + 3xL = 0 + -1L
6l + -2lx + 3xL = 0 + -1L
Remove the zero:
6l + -2lx + 3xL = -1L

Add '-6l' to each side of the equation.
6l + -2lx + -6l + 3xL = -1L + -6l

Reorder the terms:
6l + -6l + -2lx + 3xL = -1L + -6l

Combine like terms: 6l + -6l = 0
0 + -2lx + 3xL = -1L + -6l
-2lx + 3xL = -1L + -6l

Add '2lx' to each side of the equation.
-2lx + 2lx + 3xL = -1L + -6l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 3xL = -1L + -6l + 2lx
3xL = -1L + -6l + 2lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -1L + -6l + 2lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -1L + -6l + 2lx + -3xL

Simplifying
0 = -1L + -6l + 2lx + -3xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

See similar equations:

| 5x-4=6x-5 | | (r-4)(r+18)=-46 | | x/0.008-x | | 3t+19=6t+4 | | 9n+(7n+21)=59 | | 7*c=609 | | 0.5x+0.4y=50 | | 1+3(x-2)=11-9(x-6) | | 7+10k=12k+1 | | -8+4u=-28 | | 4-5y=5y-x | | 15=-7+4v | | 45m^2=9mw | | 8x+8=4x+52 | | 12x^2+2x-4= | | N^2+3N-1=3 | | 8x+3=7x-10 | | 10-2y=40 | | 45m^2=9w | | Log(x+3)+log(x)-1=0 | | 5=2p+q | | f(x)=0.41ln(x+1)+31 | | x+gy=j | | 5(2x+3)+4= | | 12m-16=44 | | b(x)+gy=j | | 14-2y=50 | | X-1/12=5/6 | | 2.9x-3+x-3= | | 4x+12=-53 | | 177+2x=1031 | | 3h+10+2h=2(6-h) |

Equations solver categories