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

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


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

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

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

Reorder the terms:
-2ln + lnx = 3ln + 2lnx + -2lnx

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

Solving
-2ln + lnx = 3ln

Solving for variable 'l'.

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

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

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

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

| 4x+15=6x+3 | | y/2=6 | | 7x-38.65=3.35 | | 60+90+2n=180 | | -2(5x+3)=-86 | | v^2=-1 | | (a^2-4a+6)+(-3a+13a+1)=0 | | 4.2z+8.5=214.3 | | p^2=-49 | | 4(8x-42)=88 | | -11=x+23 | | 6x(7x-6)-6=0 | | 5(x-2)=3x+18 | | -6.5a=325 | | 2x-3/1.12=x/5 | | -17=4v+7 | | 3800/395 | | y-(-5)=15y | | 4/7=16x | | 2w=-18 | | x=2(2)+3+2 | | -x/5=41 | | 48+66+5c+1=180 | | x=2y+3+y | | -87=3-9p | | -x^2+5x=5 | | 9a=15 | | Log(4x+3)=log(2x+13) | | -7r=338.1 | | (3a+1)(4a-4)= | | y-8.1=32.4 | | 4000-1600x=2500 |

Equations solver categories