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Simplifying lg(4x + 5) = lg(5x + 2) Reorder the terms: gl(5 + 4x) = lg(5x + 2) (5 * gl + 4x * gl) = lg(5x + 2) (5gl + 4glx) = lg(5x + 2) Reorder the terms: 5gl + 4glx = gl(2 + 5x) 5gl + 4glx = (2 * gl + 5x * gl) 5gl + 4glx = (2gl + 5glx) Solving 5gl + 4glx = 2gl + 5glx 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. 5gl + -2gl + 4glx = 2gl + -2gl + 5glx Combine like terms: 5gl + -2gl = 3gl 3gl + 4glx = 2gl + -2gl + 5glx Combine like terms: 2gl + -2gl = 0 3gl + 4glx = 0 + 5glx 3gl + 4glx = 5glx Add '-5glx' to each side of the equation. 3gl + 4glx + -5glx = 5glx + -5glx Combine like terms: 4glx + -5glx = -1glx 3gl + -1glx = 5glx + -5glx Combine like terms: 5glx + -5glx = 0 3gl + -1glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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