ln(x+40)+ln(2)=2ln(x)

Solution for ln(x+40)+ln(2)=2ln(x) equation:

Simplifying
ln(x + 40) + ln(2) = 2ln(x)

Reorder the terms:
ln(40 + x) + ln(2) = 2ln(x)
(40 * ln + x * ln) + ln(2) = 2ln(x)
(40ln + lnx) + ln(2) = 2ln(x)

Reorder the terms for easier multiplication:
40ln + lnx + 2ln = 2ln(x)

Reorder the terms:
40ln + 2ln + lnx = 2ln(x)

Combine like terms: 40ln + 2ln = 42ln
42ln + lnx = 2ln(x)

Multiply ln * x
42ln + lnx = 2lnx

Solving
42ln + lnx = 2lnx

Solving for variable 'l'.

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

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

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

Combine like terms: 2lnx + -2lnx = 0
42ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(42 + -1x) = 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 '(42 + -1x)' equal to zero and attempt to solve:

Simplifying
42 + -1x = 0

Solving
42 + -1x = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1x = 0 + -42
-1x = 0 + -42

Combine like terms: 0 + -42 = -42
-1x = -42

Add 'x' to each side of the equation.
-1x + x = -42 + x

Combine like terms: -1x + x = 0
0 = -42 + x

Simplifying
0 = -42 + x

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.