ln(5x+1)=ln(7x)

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Solution for ln(5x+1)=ln(7x) equation: 


Simplifying
ln(5x + 1) = ln(7x)

Reorder the terms:
ln(1 + 5x) = ln(7x)
(1 * ln + 5x * ln) = ln(7x)
(1ln + 5lnx) = ln(7x)

Remove parenthesis around (7x)
1ln + 5lnx = ln * 7x

Reorder the terms for easier multiplication:
1ln + 5lnx = 7ln * x

Multiply ln * x
1ln + 5lnx = 7lnx

Solving
1ln + 5lnx = 7lnx

Solving for variable 'l'.

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

Add '-7lnx' to each side of the equation.
1ln + 5lnx + -7lnx = 7lnx + -7lnx

Combine like terms: 5lnx + -7lnx = -2lnx
1ln + -2lnx = 7lnx + -7lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Add '2x' to each side of the equation.
-2x + 2x = -1 + 2x

Combine like terms: -2x + 2x = 0
0 = -1 + 2x

Simplifying
0 = -1 + 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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