ln(15)=ln(4)+ln(x+6)

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Solution for ln(15)=ln(4)+ln(x+6) equation:


Simplifying
ln(15) = ln(4) + ln(x + 6)

Reorder the terms for easier multiplication:
15ln = ln(4) + ln(x + 6)

Reorder the terms for easier multiplication:
15ln = 4ln + ln(x + 6)

Reorder the terms:
15ln = 4ln + ln(6 + x)
15ln = 4ln + (6 * ln + x * ln)
15ln = 4ln + (6ln + lnx)

Combine like terms: 4ln + 6ln = 10ln
15ln = 10ln + lnx

Solving
15ln = 10ln + lnx

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.
15ln + -10ln = 10ln + -10ln + lnx

Combine like terms: 15ln + -10ln = 5ln
5ln = 10ln + -10ln + lnx

Combine like terms: 10ln + -10ln = 0
5ln = 0 + lnx
5ln = lnx

Add '-1lnx' to each side of the equation.
5ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
5ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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