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Simplifying lg(2x + -1) = 2 + lgx + -1lg(x + -3) Reorder the terms: gl(-1 + 2x) = 2 + lgx + -1lg(x + -3) (-1 * gl + 2x * gl) = 2 + lgx + -1lg(x + -3) (-1gl + 2glx) = 2 + lgx + -1lg(x + -3) Reorder the terms: -1gl + 2glx = 2 + glx + -1gl(-3 + x) -1gl + 2glx = 2 + glx + (-3 * -1gl + x * -1gl) -1gl + 2glx = 2 + glx + (3gl + -1glx) Reorder the terms: -1gl + 2glx = 2 + 3gl + glx + -1glx Combine like terms: glx + -1glx = 0 -1gl + 2glx = 2 + 3gl + 0 -1gl + 2glx = 2 + 3gl Solving -1gl + 2glx = 2 + 3gl Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3gl' to each side of the equation. -1gl + -3gl + 2glx = 2 + 3gl + -3gl Combine like terms: -1gl + -3gl = -4gl -4gl + 2glx = 2 + 3gl + -3gl Combine like terms: 3gl + -3gl = 0 -4gl + 2glx = 2 + 0 -4gl + 2glx = 2 Reorder the terms: -2 + -4gl + 2glx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -4gl + 2glx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2gl + glx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2gl + glx)' equal to zero and attempt to solve: Simplifying -1 + -2gl + glx = 0 Solving -1 + -2gl + glx = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2gl + 1 + glx = 0 + 1 Reorder the terms: -1 + 1 + -2gl + glx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2gl + glx = 0 + 1 -2gl + glx = 0 + 1 Combine like terms: 0 + 1 = 1 -2gl + glx = 1 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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