ln*(x-15)+ln*(x+48)-3*ln*4=0

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Solution for ln*(x-15)+ln*(x+48)-3*ln*4=0 equation: 


Simplifying
ln(x + -15) + ln(x + 48) + -3ln * 4 = 0

Reorder the terms:
ln(-15 + x) + ln(x + 48) + -3ln * 4 = 0
(-15 * ln + x * ln) + ln(x + 48) + -3ln * 4 = 0
(-15ln + lnx) + ln(x + 48) + -3ln * 4 = 0

Reorder the terms:
-15ln + lnx + ln(48 + x) + -3ln * 4 = 0
-15ln + lnx + (48 * ln + x * ln) + -3ln * 4 = 0
-15ln + lnx + (48ln + lnx) + -3ln * 4 = 0

Reorder the terms for easier multiplication:
-15ln + lnx + 48ln + lnx + -3 * 4ln = 0

Multiply -3 * 4
-15ln + lnx + 48ln + lnx + -12ln = 0

Reorder the terms:
-15ln + 48ln + -12ln + lnx + lnx = 0

Combine like terms: -15ln + 48ln = 33ln
33ln + -12ln + lnx + lnx = 0

Combine like terms: 33ln + -12ln = 21ln
21ln + lnx + lnx = 0

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

Solving
21ln + 2lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(21 + 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 '(21 + 2x)' equal to zero and attempt to solve:

Simplifying
21 + 2x = 0

Solving
21 + 2x = 0

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

Add '-21' to each side of the equation.
21 + -21 + 2x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 2x = 0 + -21
2x = 0 + -21

Combine like terms: 0 + -21 = -21
2x = -21

Add '-2x' to each side of the equation.
2x + -2x = -21 + -2x

Combine like terms: 2x + -2x = 0
0 = -21 + -2x

Simplifying
0 = -21 + -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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