ln(3x+7)+ln(4)=2ln(x)

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Solution for ln(3x+7)+ln(4)=2ln(x) equation: 


Simplifying
ln(3x + 7) + ln(4) = 2ln(x)

Reorder the terms:
ln(7 + 3x) + ln(4) = 2ln(x)
(7 * ln + 3x * ln) + ln(4) = 2ln(x)
(7ln + 3lnx) + ln(4) = 2ln(x)

Reorder the terms for easier multiplication:
7ln + 3lnx + 4ln = 2ln(x)

Reorder the terms:
7ln + 4ln + 3lnx = 2ln(x)

Combine like terms: 7ln + 4ln = 11ln
11ln + 3lnx = 2ln(x)

Multiply ln * x
11ln + 3lnx = 2lnx

Solving
11ln + 3lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
11ln + 3lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 3lnx + -2lnx = 1lnx
11ln + 1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
11ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(11 + 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 '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Add '-1x' to each side of the equation.
x + -1x = -11 + -1x

Combine like terms: x + -1x = 0
0 = -11 + -1x

Simplifying
0 = -11 + -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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