ln(40x)=ln(1+x)

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Solution for ln(40x)=ln(1+x) equation: 


Simplifying
ln(40x) = ln(1 + x)

Remove parenthesis around (40x)
ln * 40x = ln(1 + x)

Reorder the terms for easier multiplication:
40ln * x = ln(1 + x)

Multiply ln * x
40lnx = ln(1 + x)
40lnx = (1 * ln + x * ln)
40lnx = (1ln + lnx)

Solving
40lnx = 1ln + lnx

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 + 40lnx = 1ln + -1ln + lnx

Combine like terms: 1ln + -1ln = 0
-1ln + 40lnx = 0 + lnx
-1ln + 40lnx = lnx

Add '-1lnx' to each side of the equation.
-1ln + 40lnx + -1lnx = lnx + -1lnx

Combine like terms: 40lnx + -1lnx = 39lnx
-1ln + 39lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + 39lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 39x) = 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 '(-1 + 39x)' equal to zero and attempt to solve:

Simplifying
-1 + 39x = 0

Solving
-1 + 39x = 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 + 39x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 39x = 0 + 1
39x = 0 + 1

Combine like terms: 0 + 1 = 1
39x = 1

Add '-39x' to each side of the equation.
39x + -39x = 1 + -39x

Combine like terms: 39x + -39x = 0
0 = 1 + -39x

Simplifying
0 = 1 + -39x

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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