ln(9X-7)=ln(5X+33)

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Solution for ln(9X-7)=ln(5X+33) equation: 


Simplifying
ln(9X + -7) = ln(5X + 33)

Reorder the terms:
ln(-7 + 9X) = ln(5X + 33)
(-7 * ln + 9X * ln) = ln(5X + 33)
(-7ln + 9lnX) = ln(5X + 33)

Reorder the terms:
-7ln + 9lnX = ln(33 + 5X)
-7ln + 9lnX = (33 * ln + 5X * ln)
-7ln + 9lnX = (33ln + 5lnX)

Solving
-7ln + 9lnX = 33ln + 5lnX

Solving for variable 'l'.

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

Add '-33ln' to each side of the equation.
-7ln + -33ln + 9lnX = 33ln + -33ln + 5lnX

Combine like terms: -7ln + -33ln = -40ln
-40ln + 9lnX = 33ln + -33ln + 5lnX

Combine like terms: 33ln + -33ln = 0
-40ln + 9lnX = 0 + 5lnX
-40ln + 9lnX = 5lnX

Add '-5lnX' to each side of the equation.
-40ln + 9lnX + -5lnX = 5lnX + -5lnX

Combine like terms: 9lnX + -5lnX = 4lnX
-40ln + 4lnX = 5lnX + -5lnX

Combine like terms: 5lnX + -5lnX = 0
-40ln + 4lnX = 0

Factor out the Greatest Common Factor (GCF), '4ln'.
4ln(-10 + X) = 0

Ignore the factor 4.

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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