(ln(x+5))-(ln(10))=(ln(13))

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Solution for (ln(x+5))-(ln(10))=(ln(13)) equation: 


Simplifying
(ln(x + 5)) + -1(ln(10)) = (ln(13))

Reorder the terms:
(ln(5 + x)) + -1(ln(10)) = (ln(13))
((5 * ln + x * ln)) + -1(ln(10)) = (ln(13))
((5ln + lnx)) + -1(ln(10)) = (ln(13))
(5ln + lnx) + -1(ln(10)) = (ln(13))

Remove parenthesis around (5ln + lnx)
5ln + lnx + -1(ln(10)) = (ln(13))

Reorder the terms for easier multiplication:
5ln + lnx + -1(10ln) = (ln(13))

Remove parenthesis around (10ln)
5ln + lnx + -1 * 10ln = (ln(13))

Multiply -1 * 10
5ln + lnx + -10ln = (ln(13))

Reorder the terms:
5ln + -10ln + lnx = (ln(13))

Combine like terms: 5ln + -10ln = -5ln
-5ln + lnx = (ln(13))

Reorder the terms for easier multiplication:
-5ln + lnx = (13ln)

Solving
-5ln + lnx = (13ln)

Solving for variable 'l'.

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

Add '(-13ln)' to each side of the equation.
-5ln + (-13ln) + lnx = (13ln) + (-13ln)

Combine like terms: -5ln + (-13ln) = -18ln
-18ln + lnx = (13ln) + (-13ln)

Combine like terms: (13ln) + (-13ln) = 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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