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Simplifying lg(8x + 9) = 2lgx Reorder the terms: gl(9 + 8x) = 2lgx (9 * gl + 8x * gl) = 2lgx (9gl + 8glx) = 2lgx Solving 9gl + 8glx = 2glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glx' to each side of the equation. 9gl + 8glx + -2glx = 2glx + -2glx Combine like terms: 8glx + -2glx = 6glx 9gl + 6glx = 2glx + -2glx Combine like terms: 2glx + -2glx = 0 9gl + 6glx = 0 Factor out the Greatest Common Factor (GCF), '3gl'. 3gl(3 + 2x) = 0 Ignore the factor 3.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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