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Simplifying lg(x) + lg(x) = lg(30x + -72) + -1lg(2) Multiply gl * x glx + lg(x) = lg(30x + -72) + -1lg(2) Multiply gl * x glx + glx = lg(30x + -72) + -1lg(2) Combine like terms: glx + glx = 2glx 2glx = lg(30x + -72) + -1lg(2) Reorder the terms: 2glx = gl(-72 + 30x) + -1lg(2) 2glx = (-72 * gl + 30x * gl) + -1lg(2) 2glx = (-72gl + 30glx) + -1lg(2) Reorder the terms for easier multiplication: 2glx = -72gl + 30glx + -1 * 2gl Multiply -1 * 2 2glx = -72gl + 30glx + -2gl Reorder the terms: 2glx = -72gl + -2gl + 30glx Combine like terms: -72gl + -2gl = -74gl 2glx = -74gl + 30glx Solving 2glx = -74gl + 30glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '74gl' to each side of the equation. 74gl + 2glx = -74gl + 74gl + 30glx Combine like terms: -74gl + 74gl = 0 74gl + 2glx = 0 + 30glx 74gl + 2glx = 30glx Add '-30glx' to each side of the equation. 74gl + 2glx + -30glx = 30glx + -30glx Combine like terms: 2glx + -30glx = -28glx 74gl + -28glx = 30glx + -30glx Combine like terms: 30glx + -30glx = 0 74gl + -28glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(37 + -14x) = 0 Ignore the factor 2.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 '(37 + -14x)' equal to zero and attempt to solve: Simplifying 37 + -14x = 0 Solving 37 + -14x = 0 Move all terms containing g to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + -14x = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -14x = 0 + -37 -14x = 0 + -37 Combine like terms: 0 + -37 = -37 -14x = -37 Add '14x' to each side of the equation. -14x + 14x = -37 + 14x Combine like terms: -14x + 14x = 0 0 = -37 + 14x Simplifying 0 = -37 + 14x 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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