2ln(x-1)=ln(3x-5)

Simple and best practice solution for 2ln(x-1)=ln(3x-5) 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 2ln(x-1)=ln(3x-5) equation:


Simplifying
2ln(x + -1) = ln(3x + -5)

Reorder the terms:
2ln(-1 + x) = ln(3x + -5)
(-1 * 2ln + x * 2ln) = ln(3x + -5)
(-2ln + 2lnx) = ln(3x + -5)

Reorder the terms:
-2ln + 2lnx = ln(-5 + 3x)
-2ln + 2lnx = (-5 * ln + 3x * ln)
-2ln + 2lnx = (-5ln + 3lnx)

Solving
-2ln + 2lnx = -5ln + 3lnx

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
-2ln + 5ln + 2lnx = -5ln + 5ln + 3lnx

Combine like terms: -2ln + 5ln = 3ln
3ln + 2lnx = -5ln + 5ln + 3lnx

Combine like terms: -5ln + 5ln = 0
3ln + 2lnx = 0 + 3lnx
3ln + 2lnx = 3lnx

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

Combine like terms: 2lnx + -3lnx = -1lnx
3ln + -1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
3ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + -1x) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

See similar equations:

| 20x-7=1+16x | | (5w+9)(5+w)=0 | | 5.7+3z=9.3 | | 5x+4y=6 | | x^4-x^2+4*x-3=0 | | 4y=6-5x | | 0.02(6t-3)=0.12(t-2)+0.18 | | x^2-17+70=0 | | 1.25x^2-5=0 | | -9=x+6 | | 9.1x-5=8.1x | | 0=2x^2-x+1 | | 3x+-12=6x+16 | | -50=4+6x | | 9x+12=-60 | | 2x+-12=8x+16 | | 80-4x=23x+17 | | -93-9x=9+15 | | 4x+-12=8x+15 | | -5+9=14x-2-13x | | .5y^2+2y-1=0 | | 3x+-12=4x+15 | | 114=2(6+w)+2w | | x(-5)=(-2) | | 114=12+4w | | 2x+4=36 | | 4x-16=8x+12 | | 6x-10=4x+12 | | 3p^2+19p+20=0 | | 20-3x=x+4 | | 3=9x+5 | | 9=5x+3 |

Equations solver categories