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Simplifying 2ln(x + 8) + lnx = ln(12x2 + 89x + 100) Reorder the terms: 2ln(8 + x) + lnx = ln(12x2 + 89x + 100) (8 * 2ln + x * 2ln) + lnx = ln(12x2 + 89x + 100) (16ln + 2lnx) + lnx = ln(12x2 + 89x + 100) Combine like terms: 2lnx + lnx = 3lnx 16ln + 3lnx = ln(12x2 + 89x + 100) Reorder the terms: 16ln + 3lnx = ln(100 + 89x + 12x2) 16ln + 3lnx = (100 * ln + 89x * ln + 12x2 * ln) 16ln + 3lnx = (100ln + 89lnx + 12lnx2) Solving 16ln + 3lnx = 100ln + 89lnx + 12lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-100ln' to each side of the equation. 16ln + -100ln + 3lnx = 100ln + 89lnx + -100ln + 12lnx2 Combine like terms: 16ln + -100ln = -84ln -84ln + 3lnx = 100ln + 89lnx + -100ln + 12lnx2 Reorder the terms: -84ln + 3lnx = 100ln + -100ln + 89lnx + 12lnx2 Combine like terms: 100ln + -100ln = 0 -84ln + 3lnx = 0 + 89lnx + 12lnx2 -84ln + 3lnx = 89lnx + 12lnx2 Add '-89lnx' to each side of the equation. -84ln + 3lnx + -89lnx = 89lnx + -89lnx + 12lnx2 Combine like terms: 3lnx + -89lnx = -86lnx -84ln + -86lnx = 89lnx + -89lnx + 12lnx2 Combine like terms: 89lnx + -89lnx = 0 -84ln + -86lnx = 0 + 12lnx2 -84ln + -86lnx = 12lnx2 Add '-12lnx2' to each side of the equation. -84ln + -86lnx + -12lnx2 = 12lnx2 + -12lnx2 Combine like terms: 12lnx2 + -12lnx2 = 0 -84ln + -86lnx + -12lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(42 + 43x + 6x2) = 0 Factor a trinomial. -2ln((6 + x)(7 + 6x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Add '-6x' to each side of the equation. 6x + -6x = -7 + -6x Combine like terms: 6x + -6x = 0 0 = -7 + -6x Simplifying 0 = -7 + -6x 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.
| 7+[4(20-7+5)]= | | x^3-0x^2-16x+32=0 | | -2y=80x-8 | | -6(5k-4)=30 | | 20(x-5)-12(5x-5)=240 | | f(x)=sin(5lnx) | | 4y+16+64=180 | | -7n-8-2n= | | (4+3i)(5-i)=0 | | 9h-h+3= | | -4(9.5y+9)=-30.5 | | 8h-3h-2= | | n-5n-4= | | 4y+16=64 | | 5=7(2x+1)+2x | | 4x-7x=2 | | 3x^2-1=6x-1 | | 7g-1-9g= | | -5+12=4x-6 | | (3x+5)+(13-3x)= | | 3y=10x+68 | | 4n+1+4n+1=180 | | 5x+7-2x=2(x-1) | | 8+2(1-5a)=-29 | | 10x+6x-59+8y= | | -6=3.10w | | .01= | | 136.06=2.45h+72.36 | | 2x+2(-x+1)=15 | | .7x+7=1.1x-2 | | 4x+8-x=20 | | D+3+d=20 |