ln(x-4)+ln(x+3)=ln(10x)

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Solution for ln(x-4)+ln(x+3)=ln(10x) equation:


Simplifying
ln(x + -4) + ln(x + 3) = ln(10x)

Reorder the terms:
ln(-4 + x) + ln(x + 3) = ln(10x)
(-4 * ln + x * ln) + ln(x + 3) = ln(10x)
(-4ln + lnx) + ln(x + 3) = ln(10x)

Reorder the terms:
-4ln + lnx + ln(3 + x) = ln(10x)
-4ln + lnx + (3 * ln + x * ln) = ln(10x)
-4ln + lnx + (3ln + lnx) = ln(10x)

Reorder the terms:
-4ln + 3ln + lnx + lnx = ln(10x)

Combine like terms: -4ln + 3ln = -1ln
-1ln + lnx + lnx = ln(10x)

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(10x)

Remove parenthesis around (10x)
-1ln + 2lnx = ln * 10x

Reorder the terms for easier multiplication:
-1ln + 2lnx = 10ln * x

Multiply ln * x
-1ln + 2lnx = 10lnx

Solving
-1ln + 2lnx = 10lnx

Solving for variable 'l'.

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

Add '-10lnx' to each side of the equation.
-1ln + 2lnx + -10lnx = 10lnx + -10lnx

Combine like terms: 2lnx + -10lnx = -8lnx
-1ln + -8lnx = 10lnx + -10lnx

Combine like terms: 10lnx + -10lnx = 0
-1ln + -8lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(1 + 8x) = 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 '(1 + 8x)' equal to zero and attempt to solve: Simplifying 1 + 8x = 0 Solving 1 + 8x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x = 0 + -1 8x = 0 + -1 Combine like terms: 0 + -1 = -1 8x = -1 Add '-8x' to each side of the equation. 8x + -8x = -1 + -8x Combine like terms: 8x + -8x = 0 0 = -1 + -8x Simplifying 0 = -1 + -8x 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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