ln(x+4)+ln(x)=ln(21)

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Solution for ln(x+4)+ln(x)=ln(21) equation: 


Simplifying
ln(x + 4) + ln(x) = ln(21)

Reorder the terms:
ln(4 + x) + ln(x) = ln(21)
(4 * ln + x * ln) + ln(x) = ln(21)
(4ln + lnx) + ln(x) = ln(21)

Multiply ln * x
4ln + lnx + lnx = ln(21)

Combine like terms: lnx + lnx = 2lnx
4ln + 2lnx = ln(21)

Reorder the terms for easier multiplication:
4ln + 2lnx = 21ln

Solving
4ln + 2lnx = 21ln

Solving for variable 'l'.

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

Add '-21ln' to each side of the equation.
4ln + -21ln + 2lnx = 21ln + -21ln

Combine like terms: 4ln + -21ln = -17ln
-17ln + 2lnx = 21ln + -21ln

Combine like terms: 21ln + -21ln = 0
-17ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-17 + 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 '(-17 + 2x)' equal to zero and attempt to solve:

Simplifying
-17 + 2x = 0

Solving
-17 + 2x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 2x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 2x = 0 + 17
2x = 0 + 17

Combine like terms: 0 + 17 = 17
2x = 17

Add '-2x' to each side of the equation.
2x + -2x = 17 + -2x

Combine like terms: 2x + -2x = 0
0 = 17 + -2x

Simplifying
0 = 17 + -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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