ln(7x+32)+ln(4)=2*ln(x)

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Solution for ln(7x+32)+ln(4)=2*ln(x) equation: 


Simplifying
ln(7x + 32) + ln(4) = 2ln(x)

Reorder the terms:
ln(32 + 7x) + ln(4) = 2ln(x)
(32 * ln + 7x * ln) + ln(4) = 2ln(x)
(32ln + 7lnx) + ln(4) = 2ln(x)

Reorder the terms for easier multiplication:
32ln + 7lnx + 4ln = 2ln(x)

Reorder the terms:
32ln + 4ln + 7lnx = 2ln(x)

Combine like terms: 32ln + 4ln = 36ln
36ln + 7lnx = 2ln(x)

Multiply ln * x
36ln + 7lnx = 2lnx

Solving
36ln + 7lnx = 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.
36ln + 7lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 7lnx + -2lnx = 5lnx
36ln + 5lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
36ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(36 + 5x) = 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 '(36 + 5x)' equal to zero and attempt to solve:

Simplifying
36 + 5x = 0

Solving
36 + 5x = 0

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

Add '-36' to each side of the equation.
36 + -36 + 5x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 5x = 0 + -36
5x = 0 + -36

Combine like terms: 0 + -36 = -36
5x = -36

Add '-5x' to each side of the equation.
5x + -5x = -36 + -5x

Combine like terms: 5x + -5x = 0
0 = -36 + -5x

Simplifying
0 = -36 + -5x

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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