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

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


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

Remove parenthesis around (5x)
ln * 5x + -1ln(x + -3) = ln(2)

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

Multiply ln * x
5lnx + -1ln(x + -3) = ln(2)

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

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

Combine like terms: 5lnx + -1lnx = 4lnx
3ln + 4lnx = ln(2)

Reorder the terms for easier multiplication:
3ln + 4lnx = 2ln

Solving
3ln + 4lnx = 2ln

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 + 4lnx = 2ln + -2ln

Combine like terms: 3ln + -2ln = 1ln
1ln + 4lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
1ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 4x) = 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 '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Add '-4x' to each side of the equation.
4x + -4x = -1 + -4x

Combine like terms: 4x + -4x = 0
0 = -1 + -4x

Simplifying
0 = -1 + -4x

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:

| 0.1429(10+x)=7 | | 15=2x-y | | 108+8y=-4y | | N+(n+1)+(n+2)+(n+3)=131 | | 2x^4+4x^3+8x=0 | | -11.3=-7y+6.2 | | 20x-45=0 | | N+(n+1)+(n+2)=55 | | 7.66(9.33-6.33)-y=2 | | -4(-5)-3y=8 | | cos(x)-cos(2x)=0 | | 30=75lb | | 3=75lb | | 2x^2-4y^2=16 | | (5y-1)(3-2y)= | | -4x-3(-11-3x)=8 | | x-3=5.79 | | 3f+10h= | | 3a+6a-2a= | | -6y=2.94 | | 0.08(y-6)+0.20y=0.12y-0.07(20) | | -6=2.94 | | N+(n+1)+(n+2)=27 | | 6x^2+30=3x(2x+5) | | ln(2x-3)+ln(x+5)=0 | | =24x^2-4x-4 | | 3(2x+3x)+4=28 | | 3x-2=28-2x | | -.99*27x=42.72 | | x/23=15/7 | | -2b=-3 | | -.99+27x=42.72 |

Equations solver categories