ln(x)-ln(3)=ln(15)

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Solution for ln(x)-ln(3)=ln(15) equation: 


Simplifying
ln(x) + -1ln(3) = ln(15)

Multiply ln * x
lnx + -1ln(3) = ln(15)

Reorder the terms for easier multiplication:
lnx + -1 * 3ln = ln(15)

Multiply -1 * 3
lnx + -3ln = ln(15)

Reorder the terms:
-3ln + lnx = ln(15)

Reorder the terms for easier multiplication:
-3ln + lnx = 15ln

Solving
-3ln + lnx = 15ln

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
-3ln + -15ln + lnx = 15ln + -15ln

Combine like terms: -3ln + -15ln = -18ln
-18ln + lnx = 15ln + -15ln

Combine like terms: 15ln + -15ln = 0
-18ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-18 + 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 '(-18 + x)' equal to zero and attempt to solve:

Simplifying
-18 + x = 0

Solving
-18 + x = 0

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

Add '18' to each side of the equation.
-18 + 18 + x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + x = 0 + 18
x = 0 + 18

Combine like terms: 0 + 18 = 18
x = 18

Add '-1x' to each side of the equation.
x + -1x = 18 + -1x

Combine like terms: x + -1x = 0
0 = 18 + -1x

Simplifying
0 = 18 + -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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