ln(2x+7)+ln(x)=ln(5)

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Solution for ln(2x+7)+ln(x)=ln(5) equation:


Simplifying
ln(2x + 7) + ln(x) = ln(5)

Reorder the terms:
ln(7 + 2x) + ln(x) = ln(5)
(7 * ln + 2x * ln) + ln(x) = ln(5)
(7ln + 2lnx) + ln(x) = ln(5)

Multiply ln * x
7ln + 2lnx + lnx = ln(5)

Combine like terms: 2lnx + lnx = 3lnx
7ln + 3lnx = ln(5)

Reorder the terms for easier multiplication:
7ln + 3lnx = 5ln

Solving
7ln + 3lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
7ln + -5ln + 3lnx = 5ln + -5ln

Combine like terms: 7ln + -5ln = 2ln
2ln + 3lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
2ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + 3x) = 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -3x 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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