Lg(x+6)=2lgx

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Solution for Lg(x+6)=2lgx equation:


Simplifying
Lg(x + 6) = 2lgx

Reorder the terms:
gL(6 + x) = 2lgx
(6 * gL + x * gL) = 2lgx
(6gL + gxL) = 2lgx

Solving
6gL + gxL = 2glx

Solving for variable 'g'.

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

Add '-2glx' to each side of the equation.
6gL + -2glx + gxL = 2glx + -2glx

Combine like terms: 2glx + -2glx = 0
6gL + -2glx + gxL = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(6L + -2lx + xL) = 0

Subproblem 1

Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0

Subproblem 2

Set the factor '(6L + -2lx + xL)' equal to zero and attempt to solve: Simplifying 6L + -2lx + xL = 0 Solving 6L + -2lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + -2lx + -6L + xL = 0 + -6L Reorder the terms: 6L + -6L + -2lx + xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + -2lx + xL = 0 + -6L -2lx + xL = 0 + -6L Remove the zero: -2lx + xL = -6L Add '2lx' to each side of the equation. -2lx + 2lx + xL = -6L + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = -6L + 2lx xL = -6L + 2lx Add '-1xL' to each side of the equation. xL + -1xL = -6L + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = -6L + 2lx + -1xL Simplifying 0 = -6L + 2lx + -1xL The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

g = {0}

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