ln(2x)+ln(x+4)=ln(10)

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Solution for ln(2x)+ln(x+4)=ln(10) equation:


Simplifying
ln(2x) + ln(x + 4) = ln(10)

Remove parenthesis around (2x)
ln * 2x + ln(x + 4) = ln(10)

Reorder the terms for easier multiplication:
2ln * x + ln(x + 4) = ln(10)

Multiply ln * x
2lnx + ln(x + 4) = ln(10)

Reorder the terms:
2lnx + ln(4 + x) = ln(10)
2lnx + (4 * ln + x * ln) = ln(10)
2lnx + (4ln + lnx) = ln(10)

Reorder the terms:
4ln + 2lnx + lnx = ln(10)

Combine like terms: 2lnx + lnx = 3lnx
4ln + 3lnx = ln(10)

Reorder the terms for easier multiplication:
4ln + 3lnx = 10ln

Solving
4ln + 3lnx = 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.
4ln + -10ln + 3lnx = 10ln + -10ln

Combine like terms: 4ln + -10ln = -6ln
-6ln + 3lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-6ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-2 + x) = 0

Ignore the factor 3.

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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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