50=10+5ln(3x+6)

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Solution for 50=10+5ln(3x+6) equation:


Simplifying
50 = 10 + 5ln(3x + 6)

Reorder the terms:
50 = 10 + 5ln(6 + 3x)
50 = 10 + (6 * 5ln + 3x * 5ln)
50 = 10 + (30ln + 15lnx)

Solving
50 = 10 + 30ln + 15lnx

Solving for variable 'l'.

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

Add '-30ln' to each side of the equation.
50 + -30ln = 10 + 30ln + -30ln + 15lnx

Combine like terms: 30ln + -30ln = 0
50 + -30ln = 10 + 0 + 15lnx
50 + -30ln = 10 + 15lnx

Add '-15lnx' to each side of the equation.
50 + -30ln + -15lnx = 10 + 15lnx + -15lnx

Combine like terms: 15lnx + -15lnx = 0
50 + -30ln + -15lnx = 10 + 0
50 + -30ln + -15lnx = 10

Add '-50' to each side of the equation.
50 + -30ln + -50 + -15lnx = 10 + -50

Reorder the terms:
50 + -50 + -30ln + -15lnx = 10 + -50

Combine like terms: 50 + -50 = 0
0 + -30ln + -15lnx = 10 + -50
-30ln + -15lnx = 10 + -50

Combine like terms: 10 + -50 = -40
-30ln + -15lnx = -40

Reorder the terms:
40 + -30ln + -15lnx = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -30ln + -15lnx = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + -6ln + -3lnx) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(8 + -6ln + -3lnx)' equal to zero and attempt to solve: Simplifying 8 + -6ln + -3lnx = 0 Solving 8 + -6ln + -3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -6ln + -8 + -3lnx = 0 + -8 Reorder the terms: 8 + -8 + -6ln + -3lnx = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6ln + -3lnx = 0 + -8 -6ln + -3lnx = 0 + -8 Combine like terms: 0 + -8 = -8 -6ln + -3lnx = -8 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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