ln(x-9)+ln(x)=ln(10)

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Solution for ln(x-9)+ln(x)=ln(10) equation: 


Simplifying
ln(x + -9) + ln(x) = ln(10)

Reorder the terms:
ln(-9 + x) + ln(x) = ln(10)
(-9 * ln + x * ln) + ln(x) = ln(10)
(-9ln + lnx) + ln(x) = ln(10)

Multiply ln * x
-9ln + lnx + lnx = ln(10)

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

Reorder the terms for easier multiplication:
-9ln + 2lnx = 10ln

Solving
-9ln + 2lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-9ln + -10ln + 2lnx = 10ln + -10ln

Combine like terms: -9ln + -10ln = -19ln
-19ln + 2lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-19ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-19 + 2x) = 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 '(-19 + 2x)' equal to zero and attempt to solve:

Simplifying
-19 + 2x = 0

Solving
-19 + 2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + 2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2x = 0 + 19
2x = 0 + 19

Combine like terms: 0 + 19 = 19
2x = 19

Add '-2x' to each side of the equation.
2x + -2x = 19 + -2x

Combine like terms: 2x + -2x = 0
0 = 19 + -2x

Simplifying
0 = 19 + -2x

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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