ln(x)+ln(3)-ln(6)=ln(10)

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Solution for ln(x)+ln(3)-ln(6)=ln(10) equation: 


Simplifying
ln(x) + ln(3) + -1ln(6) = ln(10)

Multiply ln * x
lnx + ln(3) + -1ln(6) = ln(10)

Reorder the terms for easier multiplication:
lnx + 3ln + -1ln(6) = ln(10)

Reorder the terms for easier multiplication:
lnx + 3ln + -1 * 6ln = ln(10)

Multiply -1 * 6
lnx + 3ln + -6ln = ln(10)

Reorder the terms:
3ln + -6ln + lnx = ln(10)

Combine like terms: 3ln + -6ln = -3ln
-3ln + lnx = ln(10)

Reorder the terms for easier multiplication:
-3ln + lnx = 10ln

Solving
-3ln + lnx = 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.
-3ln + -10ln + lnx = 10ln + -10ln

Combine like terms: -3ln + -10ln = -13ln
-13ln + lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-13ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-13 + 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 '(-13 + x)' equal to zero and attempt to solve:

Simplifying
-13 + x = 0

Solving
-13 + x = 0

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

Add '13' to each side of the equation.
-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x = 0 + 13
x = 0 + 13

Combine like terms: 0 + 13 = 13
x = 13

Add '-1x' to each side of the equation.
x + -1x = 13 + -1x

Combine like terms: x + -1x = 0
0 = 13 + -1x

Simplifying
0 = 13 + -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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