ln(x)+ln(x-6)=Ln(10)

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Solution for ln(x)+ln(x-6)=Ln(10) equation:


Simplifying
ln(x) + ln(x + -6) = Ln(10)

Multiply ln * x
lnx + ln(x + -6) = Ln(10)

Reorder the terms:
lnx + ln(-6 + x) = Ln(10)
lnx + (-6 * ln + x * ln) = Ln(10)
lnx + (-6ln + lnx) = Ln(10)

Reorder the terms:
-6ln + lnx + lnx = Ln(10)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = Ln(10)

Reorder the terms for easier multiplication:
-6ln + 2lnx = 10nL

Solving
-6ln + 2lnx = 10nL

Solving for variable 'l'.

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

Combine like terms: 10nL + -10nL = 0
-6ln + 2lnx + -10nL = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-3l + lx + -5L) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-3l + lx + -5L)' equal to zero and attempt to solve: Simplifying -3l + lx + -5L = 0 Reorder the terms: -5L + -3l + lx = 0 Solving -5L + -3l + lx = 0 Move all terms containing l to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + -3l + 5L + lx = 0 + 5L Reorder the terms: -5L + 5L + -3l + lx = 0 + 5L Combine like terms: -5L + 5L = 0 0 + -3l + lx = 0 + 5L -3l + lx = 0 + 5L Remove the zero: -3l + lx = 5L 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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