ln(2)=x[ln(9)-ln(2)]

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


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

Reorder the terms for easier multiplication:
2ln = x[ln(9) + -1ln(2)]

Reorder the terms for easier multiplication:
2ln = x[9ln + -1ln(2)]

Reorder the terms for easier multiplication:
2ln = x[9ln + -1 * 2ln]

Multiply -1 * 2
2ln = x[9ln + -2ln]

Combine like terms: 9ln + -2ln = 7ln
2ln = x[7ln]

Remove brackets around [7ln]
2ln = x * 7ln

Reorder the terms for easier multiplication:
2ln = 7x * ln

Multiply x * ln
2ln = 7lnx

Solving
2ln = 7lnx

Solving for variable 'l'.

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

Add '-7lnx' to each side of the equation.
2ln + -7lnx = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
2ln + -7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -7x) = 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 '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Add '7x' to each side of the equation.
-7x + 7x = -2 + 7x

Combine like terms: -7x + 7x = 0
0 = -2 + 7x

Simplifying
0 = -2 + 7x

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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