ln(x)+ln(x+1)=ln(42)

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Solution for ln(x)+ln(x+1)=ln(42) equation: 


Simplifying
ln(x) + ln(x + 1) = ln(42)

Multiply ln * x
lnx + ln(x + 1) = ln(42)

Reorder the terms:
lnx + ln(1 + x) = ln(42)
lnx + (1 * ln + x * ln) = ln(42)
lnx + (1ln + lnx) = ln(42)

Reorder the terms:
1ln + lnx + lnx = ln(42)

Combine like terms: lnx + lnx = 2lnx
1ln + 2lnx = ln(42)

Reorder the terms for easier multiplication:
1ln + 2lnx = 42ln

Solving
1ln + 2lnx = 42ln

Solving for variable 'l'.

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

Add '-42ln' to each side of the equation.
1ln + -42ln + 2lnx = 42ln + -42ln

Combine like terms: 1ln + -42ln = -41ln
-41ln + 2lnx = 42ln + -42ln

Combine like terms: 42ln + -42ln = 0
-41ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-41 + 2x) = 0


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 '(-41 + 2x)' equal to zero and attempt to solve:

Simplifying
-41 + 2x = 0

Solving
-41 + 2x = 0

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

Add '41' to each side of the equation.
-41 + 41 + 2x = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 2x = 0 + 41
2x = 0 + 41

Combine like terms: 0 + 41 = 41
2x = 41

Add '-2x' to each side of the equation.
2x + -2x = 41 + -2x

Combine like terms: 2x + -2x = 0
0 = 41 + -2x

Simplifying
0 = 41 + -2x

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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