ln(x)=ln(5)-2ln(3)

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Solution for ln(x)=ln(5)-2ln(3) equation: 


Simplifying
ln(x) = ln(5) + -2ln(3)

Multiply ln * x
lnx = ln(5) + -2ln(3)

Reorder the terms for easier multiplication:
lnx = 5ln + -2ln(3)

Reorder the terms for easier multiplication:
lnx = 5ln + -2 * 3ln

Multiply -2 * 3
lnx = 5ln + -6ln

Combine like terms: 5ln + -6ln = -1ln
lnx = -1ln

Solving
lnx = -1ln

Solving for variable 'l'.

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

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

Combine like terms: -1ln + ln = 0
ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -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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