ln(6x+37)=ln(3x+7)

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Solution for ln(6x+37)=ln(3x+7) equation: 


Simplifying
ln(6x + 37) = ln(3x + 7)

Reorder the terms:
ln(37 + 6x) = ln(3x + 7)
(37 * ln + 6x * ln) = ln(3x + 7)
(37ln + 6lnx) = ln(3x + 7)

Reorder the terms:
37ln + 6lnx = ln(7 + 3x)
37ln + 6lnx = (7 * ln + 3x * ln)
37ln + 6lnx = (7ln + 3lnx)

Solving
37ln + 6lnx = 7ln + 3lnx

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
37ln + -7ln + 6lnx = 7ln + -7ln + 3lnx

Combine like terms: 37ln + -7ln = 30ln
30ln + 6lnx = 7ln + -7ln + 3lnx

Combine like terms: 7ln + -7ln = 0
30ln + 6lnx = 0 + 3lnx
30ln + 6lnx = 3lnx

Add '-3lnx' to each side of the equation.
30ln + 6lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 6lnx + -3lnx = 3lnx
30ln + 3lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
30ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(10 + 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Add '-1x' to each side of the equation.
x + -1x = -10 + -1x

Combine like terms: x + -1x = 0
0 = -10 + -1x

Simplifying
0 = -10 + -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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