Ln(x-10)+ln(x-2)=0

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Solution for Ln(x-10)+ln(x-2)=0 equation:


Simplifying
Ln(x + -10) + ln(x + -2) = 0

Reorder the terms:
nL(-10 + x) + ln(x + -2) = 0
(-10 * nL + x * nL) + ln(x + -2) = 0
(-10nL + nxL) + ln(x + -2) = 0

Reorder the terms:
-10nL + nxL + ln(-2 + x) = 0
-10nL + nxL + (-2 * ln + x * ln) = 0
-10nL + nxL + (-2ln + lnx) = 0

Reorder the terms:
-2ln + lnx + -10nL + nxL = 0

Solving
-2ln + lnx + -10nL + nxL = 0

Solving for variable 'l'.

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

Add '10nL' to each side of the equation.
-2ln + lnx + -10nL + 10nL + nxL = 0 + 10nL

Combine like terms: -10nL + 10nL = 0
-2ln + lnx + 0 + nxL = 0 + 10nL
-2ln + lnx + nxL = 0 + 10nL
Remove the zero:
-2ln + lnx + nxL = 10nL

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

Combine like terms: nxL + -1nxL = 0
-2ln + lnx + 0 = 10nL + -1nxL
-2ln + lnx = 10nL + -1nxL

Reorder the terms:
-2ln + lnx + -10nL + nxL = 10nL + -10nL + -1nxL + nxL

Combine like terms: 10nL + -10nL = 0
-2ln + lnx + -10nL + nxL = 0 + -1nxL + nxL
-2ln + lnx + -10nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
-2ln + lnx + -10nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2l + lx + -10L + xL) = 0

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 '(-2l + lx + -10L + xL)' equal to zero and attempt to solve: Simplifying -2l + lx + -10L + xL = 0 Reorder the terms: -10L + -2l + lx + xL = 0 Solving -10L + -2l + lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '10L' to each side of the equation. -10L + -2l + lx + 10L + xL = 0 + 10L Reorder the terms: -10L + 10L + -2l + lx + xL = 0 + 10L Combine like terms: -10L + 10L = 0 0 + -2l + lx + xL = 0 + 10L -2l + lx + xL = 0 + 10L Remove the zero: -2l + lx + xL = 10L Add '-1xL' to each side of the equation. -2l + lx + xL + -1xL = 10L + -1xL Combine like terms: xL + -1xL = 0 -2l + lx + 0 = 10L + -1xL -2l + lx = 10L + -1xL 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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