ln(4x+9)=ln(3x-1)

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Solution for ln(4x+9)=ln(3x-1) equation: 


Simplifying
ln(4x + 9) = ln(3x + -1)

Reorder the terms:
ln(9 + 4x) = ln(3x + -1)
(9 * ln + 4x * ln) = ln(3x + -1)
(9ln + 4lnx) = ln(3x + -1)

Reorder the terms:
9ln + 4lnx = ln(-1 + 3x)
9ln + 4lnx = (-1 * ln + 3x * ln)
9ln + 4lnx = (-1ln + 3lnx)

Solving
9ln + 4lnx = -1ln + 3lnx

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
9ln + ln + 4lnx = -1ln + ln + 3lnx

Combine like terms: 9ln + ln = 10ln
10ln + 4lnx = -1ln + ln + 3lnx

Combine like terms: -1ln + ln = 0
10ln + 4lnx = 0 + 3lnx
10ln + 4lnx = 3lnx

Add '-3lnx' to each side of the equation.
10ln + 4lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 4lnx + -3lnx = 1lnx
10ln + 1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
10ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Add '-1x' to each side of the equation.
x + -1x = -10 + -1x

Combine like terms: x + -1x = 0
0 = -10 + -1x

Simplifying
0 = -10 + -1x

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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