ln(7x+4)-ln(2)=2ln(x)

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Solution for ln(7x+4)-ln(2)=2ln(x) equation: 


Simplifying
ln(7x + 4) + -1ln(2) = 2ln(x)

Reorder the terms:
ln(4 + 7x) + -1ln(2) = 2ln(x)
(4 * ln + 7x * ln) + -1ln(2) = 2ln(x)
(4ln + 7lnx) + -1ln(2) = 2ln(x)

Reorder the terms for easier multiplication:
4ln + 7lnx + -1 * 2ln = 2ln(x)

Multiply -1 * 2
4ln + 7lnx + -2ln = 2ln(x)

Reorder the terms:
4ln + -2ln + 7lnx = 2ln(x)

Combine like terms: 4ln + -2ln = 2ln
2ln + 7lnx = 2ln(x)

Multiply ln * x
2ln + 7lnx = 2lnx

Solving
2ln + 7lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
2ln + 7lnx + -2lnx = 2lnx + -2lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + 5x) = 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 '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Add '-5x' to each side of the equation.
5x + -5x = -2 + -5x

Combine like terms: 5x + -5x = 0
0 = -2 + -5x

Simplifying
0 = -2 + -5x

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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