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