ln(5x+18)+ln(3)=2*ln(x)

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Solution for ln(5x+18)+ln(3)=2*ln(x) equation: 


Simplifying
ln(5x + 18) + ln(3) = 2ln(x)

Reorder the terms:
ln(18 + 5x) + ln(3) = 2ln(x)
(18 * ln + 5x * ln) + ln(3) = 2ln(x)
(18ln + 5lnx) + ln(3) = 2ln(x)

Reorder the terms for easier multiplication:
18ln + 5lnx + 3ln = 2ln(x)

Reorder the terms:
18ln + 3ln + 5lnx = 2ln(x)

Combine like terms: 18ln + 3ln = 21ln
21ln + 5lnx = 2ln(x)

Multiply ln * x
21ln + 5lnx = 2lnx

Solving
21ln + 5lnx = 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.
21ln + 5lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 5lnx + -2lnx = 3lnx
21ln + 3lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
21ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(7 + x) = 0

Ignore the factor 3.

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 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

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

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

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

Add '-1x' to each side of the equation.
x + -1x = -7 + -1x

Combine like terms: x + -1x = 0
0 = -7 + -1x

Simplifying
0 = -7 + -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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