ln(2x+5)=ln(x-15)

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Solution for ln(2x+5)=ln(x-15) equation: 


Simplifying
ln(2x + 5) = ln(x + -15)

Reorder the terms:
ln(5 + 2x) = ln(x + -15)
(5 * ln + 2x * ln) = ln(x + -15)
(5ln + 2lnx) = ln(x + -15)

Reorder the terms:
5ln + 2lnx = ln(-15 + x)
5ln + 2lnx = (-15 * ln + x * ln)
5ln + 2lnx = (-15ln + lnx)

Solving
5ln + 2lnx = -15ln + lnx

Solving for variable 'l'.

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

Add '15ln' to each side of the equation.
5ln + 15ln + 2lnx = -15ln + 15ln + lnx

Combine like terms: 5ln + 15ln = 20ln
20ln + 2lnx = -15ln + 15ln + lnx

Combine like terms: -15ln + 15ln = 0
20ln + 2lnx = 0 + lnx
20ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
20ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
20ln + 1lnx = lnx + -1lnx

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

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

Simplifying
20 + x = 0

Solving
20 + x = 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 + x = 0 + -20

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

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

Add '-1x' to each side of the equation.
x + -1x = -20 + -1x

Combine like terms: x + -1x = 0
0 = -20 + -1x

Simplifying
0 = -20 + -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.

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