ln(6x-1)+ln(x)=ln(4)

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Solution for ln(6x-1)+ln(x)=ln(4) equation: 


Simplifying
ln(6x + -1) + ln(x) = ln(4)

Reorder the terms:
ln(-1 + 6x) + ln(x) = ln(4)
(-1 * ln + 6x * ln) + ln(x) = ln(4)
(-1ln + 6lnx) + ln(x) = ln(4)

Multiply ln * x
-1ln + 6lnx + lnx = ln(4)

Combine like terms: 6lnx + lnx = 7lnx
-1ln + 7lnx = ln(4)

Reorder the terms for easier multiplication:
-1ln + 7lnx = 4ln

Solving
-1ln + 7lnx = 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.
-1ln + -4ln + 7lnx = 4ln + -4ln

Combine like terms: -1ln + -4ln = -5ln
-5ln + 7lnx = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
-5ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 7x) = 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 '(-5 + 7x)' equal to zero and attempt to solve:

Simplifying
-5 + 7x = 0

Solving
-5 + 7x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 7x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7x = 0 + 5
7x = 0 + 5

Combine like terms: 0 + 5 = 5
7x = 5

Add '-7x' to each side of the equation.
7x + -7x = 5 + -7x

Combine like terms: 7x + -7x = 0
0 = 5 + -7x

Simplifying
0 = 5 + -7x

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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