-ln(5x+1)=lnx

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Solution for -ln(5x+1)=lnx equation: 


Simplifying
-1ln(5x + 1) = lnx

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

Solving
-1ln + -5lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-1ln + -5lnx + -1lnx = lnx + -1lnx

Combine like terms: -5lnx + -1lnx = -6lnx
-1ln + -6lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + -6lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(1 + 6x) = 0

Ignore the factor -1.

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 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x = 0 + -1
6x = 0 + -1

Combine like terms: 0 + -1 = -1
6x = -1

Add '-6x' to each side of the equation.
6x + -6x = -1 + -6x

Combine like terms: 6x + -6x = 0
0 = -1 + -6x

Simplifying
0 = -1 + -6x

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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