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Simplifying 2lgx = lg(4x + 5) Reorder the terms: 2glx = gl(5 + 4x) 2glx = (5 * gl + 4x * gl) 2glx = (5gl + 4glx) Solving 2glx = 5gl + 4glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5gl' to each side of the equation. -5gl + 2glx = 5gl + -5gl + 4glx Combine like terms: 5gl + -5gl = 0 -5gl + 2glx = 0 + 4glx -5gl + 2glx = 4glx Add '-4glx' to each side of the equation. -5gl + 2glx + -4glx = 4glx + -4glx Combine like terms: 2glx + -4glx = -2glx -5gl + -2glx = 4glx + -4glx Combine like terms: 4glx + -4glx = 0 -5gl + -2glx = 0 Factor out the Greatest Common Factor (GCF), '-1gl'. -1gl(5 + 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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -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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