ln(3x-11)+ln(x)=ln(4)

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Solution for ln(3x-11)+ln(x)=ln(4) equation: 


Simplifying
ln(3x + -11) + ln(x) = ln(4)

Reorder the terms:
ln(-11 + 3x) + ln(x) = ln(4)
(-11 * ln + 3x * ln) + ln(x) = ln(4)
(-11ln + 3lnx) + ln(x) = ln(4)

Multiply ln * x
-11ln + 3lnx + lnx = ln(4)

Combine like terms: 3lnx + lnx = 4lnx
-11ln + 4lnx = ln(4)

Reorder the terms for easier multiplication:
-11ln + 4lnx = 4ln

Solving
-11ln + 4lnx = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-11ln + -4ln + 4lnx = 4ln + -4ln

Combine like terms: -11ln + -4ln = -15ln
-15ln + 4lnx = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
-15ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-15 + 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 '(-15 + 4x)' equal to zero and attempt to solve:

Simplifying
-15 + 4x = 0

Solving
-15 + 4x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 4x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 4x = 0 + 15
4x = 0 + 15

Combine like terms: 0 + 15 = 15
4x = 15

Add '-4x' to each side of the equation.
4x + -4x = 15 + -4x

Combine like terms: 4x + -4x = 0
0 = 15 + -4x

Simplifying
0 = 15 + -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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