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Simplifying lg(6 + -1x) = 2lgx (6 * gl + -1x * gl) = 2lgx (6gl + -1glx) = 2lgx Solving 6gl + -1glx = 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 + -1glx + -2glx = 2glx + -2glx Combine like terms: -1glx + -2glx = -3glx 6gl + -3glx = 2glx + -2glx Combine like terms: 2glx + -2glx = 0 6gl + -3glx = 0 Factor out the Greatest Common Factor (GCF), '3gl'. 3gl(2 + -1x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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