ln(7x-10)=ln(5x+11)

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Solution for ln(7x-10)=ln(5x+11) equation: 


Simplifying
ln(7x + -10) = ln(5x + 11)

Reorder the terms:
ln(-10 + 7x) = ln(5x + 11)
(-10 * ln + 7x * ln) = ln(5x + 11)
(-10ln + 7lnx) = ln(5x + 11)

Reorder the terms:
-10ln + 7lnx = ln(11 + 5x)
-10ln + 7lnx = (11 * ln + 5x * ln)
-10ln + 7lnx = (11ln + 5lnx)

Solving
-10ln + 7lnx = 11ln + 5lnx

Solving for variable 'l'.

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

Add '-11ln' to each side of the equation.
-10ln + -11ln + 7lnx = 11ln + -11ln + 5lnx

Combine like terms: -10ln + -11ln = -21ln
-21ln + 7lnx = 11ln + -11ln + 5lnx

Combine like terms: 11ln + -11ln = 0
-21ln + 7lnx = 0 + 5lnx
-21ln + 7lnx = 5lnx

Add '-5lnx' to each side of the equation.
-21ln + 7lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 7lnx + -5lnx = 2lnx
-21ln + 2lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-21ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 2x) = 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 '(-21 + 2x)' equal to zero and attempt to solve:

Simplifying
-21 + 2x = 0

Solving
-21 + 2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 0 + 21
2x = 0 + 21

Combine like terms: 0 + 21 = 21
2x = 21

Add '-2x' to each side of the equation.
2x + -2x = 21 + -2x

Combine like terms: 2x + -2x = 0
0 = 21 + -2x

Simplifying
0 = 21 + -2x

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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