ln(2x-1)=ln(9)

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Solution for ln(2x-1)=ln(9) equation: 


Simplifying
ln(2x + -1) = ln(9)

Reorder the terms:
ln(-1 + 2x) = ln(9)
(-1 * ln + 2x * ln) = ln(9)
(-1ln + 2lnx) = ln(9)

Reorder the terms for easier multiplication:
-1ln + 2lnx = 9ln

Solving
-1ln + 2lnx = 9ln

Solving for variable 'l'.

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

Add '-9ln' to each side of the equation.
-1ln + -9ln + 2lnx = 9ln + -9ln

Combine like terms: -1ln + -9ln = -10ln
-10ln + 2lnx = 9ln + -9ln

Combine like terms: 9ln + -9ln = 0
-10ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-5 + x) = 0

Ignore the factor 2.

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 '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Add '-1x' to each side of the equation.
x + -1x = 5 + -1x

Combine like terms: x + -1x = 0
0 = 5 + -1x

Simplifying
0 = 5 + -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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