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