ln(10+x)=ln(3+4x)

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Solution for ln(10+x)=ln(3+4x) equation: 


Simplifying
ln(10 + x) = ln(3 + 4x)
(10 * ln + x * ln) = ln(3 + 4x)
(10ln + lnx) = ln(3 + 4x)
10ln + lnx = (3 * ln + 4x * ln)
10ln + lnx = (3ln + 4lnx)

Solving
10ln + lnx = 3ln + 4lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
10ln + -3ln + lnx = 3ln + -3ln + 4lnx

Combine like terms: 10ln + -3ln = 7ln
7ln + lnx = 3ln + -3ln + 4lnx

Combine like terms: 3ln + -3ln = 0
7ln + lnx = 0 + 4lnx
7ln + lnx = 4lnx

Add '-4lnx' to each side of the equation.
7ln + lnx + -4lnx = 4lnx + -4lnx

Combine like terms: lnx + -4lnx = -3lnx
7ln + -3lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
7ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + -3x) = 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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Add '3x' to each side of the equation.
-3x + 3x = -7 + 3x

Combine like terms: -3x + 3x = 0
0 = -7 + 3x

Simplifying
0 = -7 + 3x

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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