ln(7x+1)=ln(2-x)

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Solution for ln(7x+1)=ln(2-x) equation: 


Simplifying
ln(7x + 1) = ln(2 + -1x)

Reorder the terms:
ln(1 + 7x) = ln(2 + -1x)
(1 * ln + 7x * ln) = ln(2 + -1x)
(1ln + 7lnx) = ln(2 + -1x)
1ln + 7lnx = (2 * ln + -1x * ln)
1ln + 7lnx = (2ln + -1lnx)

Solving
1ln + 7lnx = 2ln + -1lnx

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.
1ln + -2ln + 7lnx = 2ln + -2ln + -1lnx

Combine like terms: 1ln + -2ln = -1ln
-1ln + 7lnx = 2ln + -2ln + -1lnx

Combine like terms: 2ln + -2ln = 0
-1ln + 7lnx = 0 + -1lnx
-1ln + 7lnx = -1lnx

Add 'lnx' to each side of the equation.
-1ln + 7lnx + lnx = -1lnx + lnx

Combine like terms: 7lnx + lnx = 8lnx
-1ln + 8lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-1ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 8x) = 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 + 8x)' equal to zero and attempt to solve:

Simplifying
-1 + 8x = 0

Solving
-1 + 8x = 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 + 8x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8x = 0 + 1
8x = 0 + 1

Combine like terms: 0 + 1 = 1
8x = 1

Add '-8x' to each side of the equation.
8x + -8x = 1 + -8x

Combine like terms: 8x + -8x = 0
0 = 1 + -8x

Simplifying
0 = 1 + -8x

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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