ln(2x+3)=ln(x-2)

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


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

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

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

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

Solving for variable 'l'.

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

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

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

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

Add '-1lnx' to each side of the equation.
5ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
5ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
5ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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:

| 4m+3m=0 | | 3x+199=10x-11 | | 5v=v-28 | | 18m^2=24m | | (3-7i)-(-5-5i)= | | 26-x=x+8 | | 30-7x=.5(18x-4) | | 3(7+1)= | | x^2=7-24*i | | 3x=32-4x-29 | | 262=2*3.14*R | | x^2-14x=-17 | | 13+8=x | | Y=2cos^2x-1 | | 9x^2+kx+64=0 | | 5x+2x-9=90 | | x^2+7x=-18 | | k(n)=-11n+9 | | Cos(60)=x/500 | | -6x+5-7(x-1)=-(5x-4)-7x+7 | | 2(p-5)=4(p-1) | | -15x^2+98x-140=0 | | x-(x*0.1)=600000 | | 5x+6(x-13)=5(x-12) | | 4/3(3.14)4^3 | | 7x-4x+15=2x+8 | | 25(4x+9)=180 | | 9=55*5+3x*2x | | 5(2x-3)/4-4(x-2)/3=1/2 | | 7m=12+3m | | -1/2-3/5v=1/3 | | 4418x-10293y=0 |

Equations solver categories