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

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


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

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

Remove parenthesis around (2x)
-7ln + 4lnx + ln * 2x = 2ln(x)

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

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

Combine like terms: 4lnx + 2lnx = 6lnx
-7ln + 6lnx = 2ln(x)

Multiply ln * x
-7ln + 6lnx = 2lnx

Solving
-7ln + 6lnx = 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.
-7ln + 6lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 6lnx + -2lnx = 4lnx
-7ln + 4lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-7ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 4x) = 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 '(-7 + 4x)' equal to zero and attempt to solve:

Simplifying
-7 + 4x = 0

Solving
-7 + 4x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 0 + 7
4x = 0 + 7

Combine like terms: 0 + 7 = 7
4x = 7

Add '-4x' to each side of the equation.
4x + -4x = 7 + -4x

Combine like terms: 4x + -4x = 0
0 = 7 + -4x

Simplifying
0 = 7 + -4x

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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