Solve for lnx+ln(x+3)=ln(20-5x)
Answers
Answer:
Solution for ln(x)+ln(x+3)=In(20-5x) equation:
Simplifying
ln(x) + ln(x + 3) = In(20 + -5x)
Multiply ln * x
lnx + ln(x + 3) = In(20 + -5x)
Reorder the terms:
lnx + ln(3 + x) = In(20 + -5x)
lnx + (3 * ln + x * ln) = In(20 + -5x)
lnx + (3ln + lnx) = In(20 + -5x)
Reorder the terms:
3ln + lnx + lnx = In(20 + -5x)
Combine like terms: lnx + lnx = 2lnx
3ln + 2lnx = In(20 + -5x)
3ln + 2lnx = (20 * nI + -5x * nI)
3ln + 2lnx = (20nI + -5nxI)
Solving
3ln + 2lnx = 20nI + -5nxI
Solving for variable 'l'.
Move all terms containing l to the left, all other terms to the right.
Reorder the terms:
3ln + 2lnx + -20nI + 5nxI = 20nI + -20nI + -5nxI + 5nxI
Combine like terms: 20nI + -20nI = 0
3ln + 2lnx + -20nI + 5nxI = 0 + -5nxI + 5nxI
3ln + 2lnx + -20nI + 5nxI = -5nxI + 5nxI
Combine like terms: -5nxI + 5nxI = 0
3ln + 2lnx + -20nI + 5nxI = 0
Factor out the Greatest Common Factor (GCF), 'n'.
n(3l + 2lx + -20I + 5xI) = 0
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:
Simplifying
n = 0
Solving
n = 0
Move all terms containing l to the left, all other terms to the right.
Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n
Simplifying
0 = -1n
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 '(3l + 2lx + -20I + 5xI)' equal to zero and attempt to solve:
Simplifying
3l + 2lx + -20I + 5xI = 0
Reorder the terms:
-20I + 3l + 2lx + 5xI = 0
Solving
-20I + 3l + 2lx + 5xI = 0
Move all terms containing l to the left, all other terms to the right.
Add '20I' to each side of the equation.
-20I + 3l + 2lx + 20I + 5xI = 0 + 20I
Reorder the terms:
-20I + 20I + 3l + 2lx + 5xI = 0 + 20I
Combine like terms: -20I + 20I = 0
0 + 3l + 2lx + 5xI = 0 + 20I
3l + 2lx + 5xI = 0 + 20I
Remove the zero:
3l + 2lx + 5xI = 20I
Add '-5xI' to each side of the equation.
3l + 2lx + 5xI + -5xI = 20I + -5xI
Combine like terms: 5xI + -5xI = 0
3l + 2lx + 0 = 20I + -5xI
3l + 2lx = 20I + -5xI
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.