ln(4x-10)=ln(x+10)

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Solution for ln(4x-10)=ln(x+10) equation: 


Simplifying
ln(4x + -10) = ln(x + 10)

Reorder the terms:
ln(-10 + 4x) = ln(x + 10)
(-10 * ln + 4x * ln) = ln(x + 10)
(-10ln + 4lnx) = ln(x + 10)

Reorder the terms:
-10ln + 4lnx = ln(10 + x)
-10ln + 4lnx = (10 * ln + x * ln)
-10ln + 4lnx = (10ln + lnx)

Solving
-10ln + 4lnx = 10ln + lnx

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-10ln + -10ln + 4lnx = 10ln + -10ln + lnx

Combine like terms: -10ln + -10ln = -20ln
-20ln + 4lnx = 10ln + -10ln + lnx

Combine like terms: 10ln + -10ln = 0
-20ln + 4lnx = 0 + lnx
-20ln + 4lnx = lnx

Add '-1lnx' to each side of the equation.
-20ln + 4lnx + -1lnx = lnx + -1lnx

Combine like terms: 4lnx + -1lnx = 3lnx
-20ln + 3lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-20ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-20 + 3x) = 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 '(-20 + 3x)' equal to zero and attempt to solve:

Simplifying
-20 + 3x = 0

Solving
-20 + 3x = 0

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

Add '20' to each side of the equation.
-20 + 20 + 3x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3x = 0 + 20
3x = 0 + 20

Combine like terms: 0 + 20 = 20
3x = 20

Add '-3x' to each side of the equation.
3x + -3x = 20 + -3x

Combine like terms: 3x + -3x = 0
0 = 20 + -3x

Simplifying
0 = 20 + -3x

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.

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