ln(5x-7)-4ln(3x-14)=

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Solution for ln(5x-7)-4ln(3x-14)= equation: 


Simplifying
ln(5x + -7) + -4ln(3x + -14) = 0

Reorder the terms:
ln(-7 + 5x) + -4ln(3x + -14) = 0
(-7 * ln + 5x * ln) + -4ln(3x + -14) = 0
(-7ln + 5lnx) + -4ln(3x + -14) = 0

Reorder the terms:
-7ln + 5lnx + -4ln(-14 + 3x) = 0
-7ln + 5lnx + (-14 * -4ln + 3x * -4ln) = 0
-7ln + 5lnx + (56ln + -12lnx) = 0

Reorder the terms:
-7ln + 56ln + 5lnx + -12lnx = 0

Combine like terms: -7ln + 56ln = 49ln
49ln + 5lnx + -12lnx = 0

Combine like terms: 5lnx + -12lnx = -7lnx
49ln + -7lnx = 0

Solving
49ln + -7lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), '7ln'.
7ln(7 + -1x) = 0

Ignore the factor 7.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

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

Combine like terms: -1x + x = 0
0 = -7 + x

Simplifying
0 = -7 + x

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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