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Simplifying 3ln(2x) + -1ln(4x) = ln(3x + 1) Remove parenthesis around (2x) 3ln * 2x + -1ln(4x) = ln(3x + 1) Reorder the terms for easier multiplication: 3 * 2ln * x + -1ln(4x) = ln(3x + 1) Multiply 3 * 2 6ln * x + -1ln(4x) = ln(3x + 1) Multiply ln * x 6lnx + -1ln(4x) = ln(3x + 1) Remove parenthesis around (4x) 6lnx + -1ln * 4x = ln(3x + 1) Reorder the terms for easier multiplication: 6lnx + -1 * 4ln * x = ln(3x + 1) Multiply -1 * 4 6lnx + -4ln * x = ln(3x + 1) Multiply ln * x 6lnx + -4lnx = ln(3x + 1) Combine like terms: 6lnx + -4lnx = 2lnx 2lnx = ln(3x + 1) Reorder the terms: 2lnx = ln(1 + 3x) 2lnx = (1 * ln + 3x * ln) 2lnx = (1ln + 3lnx) Solving 2lnx = 1ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -1ln + 2lnx = 1ln + -1ln + 3lnx Combine like terms: 1ln + -1ln = 0 -1ln + 2lnx = 0 + 3lnx -1ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. -1ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx -1ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + x) = 0 Ignore the factor -1.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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.
| 10345.5464=4*3.14*r^2 | | a/16+101=99 | | -36=n+(-16) | | r-6+4r=19 | | 585+0.13x=850 | | v-(-20)=29 | | 7x-4=2x+31 | | 7x-4=2x+13 | | 5x^2-9x-10=0 | | 5024=4*3.14*r^2 | | a/6+101=99 | | (y^6)/(y^10) | | 2x^3+18x^2-16x=0 | | 1/2x+7=2x+4 | | Y=200+11x | | 3x^2-24x-8=0 | | -5x-20=-5(x+2) | | (6y-6)+4y=84 | | -4-5y=-15 | | 1436.0267=4/3*3.14*r^3 | | -2(x-7)=48 | | 2(x-7)=48 | | a/3b+5b=23 | | d=c+8 | | 19=-27+z | | -1+2y=-2 | | 4x+4=14+3x | | 26=t+25 | | 65.4167=4/3*3.14*r^3 | | 2-x=x^2+8x+16 | | 65.4167=4/3*3.14-r^3 | | 25657.9322=4/3*3.14*r^3 |