Ln(x)+ln(7-x)=ln(10)

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Solution for Ln(x)+ln(7-x)=ln(10) equation: 


Simplifying
Ln(x) + ln(7 + -1x) = ln(10)

Multiply nL * x
nxL + ln(7 + -1x) = ln(10)
nxL + (7 * ln + -1x * ln) = ln(10)
nxL + (7ln + -1lnx) = ln(10)

Reorder the terms:
7ln + -1lnx + nxL = ln(10)

Reorder the terms for easier multiplication:
7ln + -1lnx + nxL = 10ln

Solving
7ln + -1lnx + nxL = 10ln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-10ln' to each side of the equation.
7ln + -1lnx + -10ln + nxL = 10ln + -10ln

Reorder the terms:
7ln + -10ln + -1lnx + nxL = 10ln + -10ln

Combine like terms: 7ln + -10ln = -3ln
-3ln + -1lnx + nxL = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-3ln + -1lnx + nxL = 0

Add '-1nxL' to each side of the equation.
-3ln + -1lnx + nxL + -1nxL = 0 + -1nxL

Combine like terms: nxL + -1nxL = 0
-3ln + -1lnx + 0 = 0 + -1nxL
-3ln + -1lnx = 0 + -1nxL
Remove the zero:
-3ln + -1lnx = -1nxL

Combine like terms: -1nxL + nxL = 0
-3ln + -1lnx + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3l + -1lx + xL) = 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 + -1lx + xL)' equal to zero and attempt to solve:

Simplifying
-3l + -1lx + xL = 0

Solving
-3l + -1lx + xL = 0

Move all terms containing l to the left, all other terms to the right.

Add '-1xL' to each side of the equation.
-3l + -1lx + xL + -1xL = 0 + -1xL

Combine like terms: xL + -1xL = 0
-3l + -1lx + 0 = 0 + -1xL
-3l + -1lx = 0 + -1xL
Remove the zero:
-3l + -1lx = -1xL

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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