lnx+2ln(x+1)=ln(x+4)+ln(3x+5)

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Solution for lnx+2ln(x+1)=ln(x+4)+ln(3x+5) equation:


Simplifying
lnx + 2ln(x + 1) = ln(x + 4) + ln(3x + 5)

Reorder the terms:
lnx + 2ln(1 + x) = ln(x + 4) + ln(3x + 5)
lnx + (1 * 2ln + x * 2ln) = ln(x + 4) + ln(3x + 5)
lnx + (2ln + 2lnx) = ln(x + 4) + ln(3x + 5)

Reorder the terms:
2ln + lnx + 2lnx = ln(x + 4) + ln(3x + 5)

Combine like terms: lnx + 2lnx = 3lnx
2ln + 3lnx = ln(x + 4) + ln(3x + 5)

Reorder the terms:
2ln + 3lnx = ln(4 + x) + ln(3x + 5)
2ln + 3lnx = (4 * ln + x * ln) + ln(3x + 5)
2ln + 3lnx = (4ln + lnx) + ln(3x + 5)

Reorder the terms:
2ln + 3lnx = 4ln + lnx + ln(5 + 3x)
2ln + 3lnx = 4ln + lnx + (5 * ln + 3x * ln)
2ln + 3lnx = 4ln + lnx + (5ln + 3lnx)

Reorder the terms:
2ln + 3lnx = 4ln + 5ln + lnx + 3lnx

Combine like terms: 4ln + 5ln = 9ln
2ln + 3lnx = 9ln + lnx + 3lnx

Combine like terms: lnx + 3lnx = 4lnx
2ln + 3lnx = 9ln + 4lnx

Solving
2ln + 3lnx = 9ln + 4lnx

Solving for variable 'l'.

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

Add '-9ln' to each side of the equation.
2ln + -9ln + 3lnx = 9ln + -9ln + 4lnx

Combine like terms: 2ln + -9ln = -7ln
-7ln + 3lnx = 9ln + -9ln + 4lnx

Combine like terms: 9ln + -9ln = 0
-7ln + 3lnx = 0 + 4lnx
-7ln + 3lnx = 4lnx

Add '-4lnx' to each side of the equation.
-7ln + 3lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 3lnx + -4lnx = -1lnx
-7ln + -1lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-7ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(7 + x) = 0

Ignore the factor -1.

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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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