ln(4x+9)=2ln(x+1)

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Solution for ln(4x+9)=2ln(x+1) equation: 


Simplifying
ln(4x + 9) = 2ln(x + 1)

Reorder the terms:
ln(9 + 4x) = 2ln(x + 1)
(9 * ln + 4x * ln) = 2ln(x + 1)
(9ln + 4lnx) = 2ln(x + 1)

Reorder the terms:
9ln + 4lnx = 2ln(1 + x)
9ln + 4lnx = (1 * 2ln + x * 2ln)
9ln + 4lnx = (2ln + 2lnx)

Solving
9ln + 4lnx = 2ln + 2lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
9ln + -2ln + 4lnx = 2ln + -2ln + 2lnx

Combine like terms: 9ln + -2ln = 7ln
7ln + 4lnx = 2ln + -2ln + 2lnx

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

Add '-2lnx' to each side of the equation.
7ln + 4lnx + -2lnx = 2lnx + -2lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Add '-2x' to each side of the equation.
2x + -2x = -7 + -2x

Combine like terms: 2x + -2x = 0
0 = -7 + -2x

Simplifying
0 = -7 + -2x

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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