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