ln(40x)=21ln(1+x)

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Solution for ln(40x)=21ln(1+x) equation: 


Simplifying
ln(40x) = 21ln(1 + x)

Remove parenthesis around (40x)
ln * 40x = 21ln(1 + x)

Reorder the terms for easier multiplication:
40ln * x = 21ln(1 + x)

Multiply ln * x
40lnx = 21ln(1 + x)
40lnx = (1 * 21ln + x * 21ln)
40lnx = (21ln + 21lnx)

Solving
40lnx = 21ln + 21lnx

Solving for variable 'l'.

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

Add '-21ln' to each side of the equation.
-21ln + 40lnx = 21ln + -21ln + 21lnx

Combine like terms: 21ln + -21ln = 0
-21ln + 40lnx = 0 + 21lnx
-21ln + 40lnx = 21lnx

Add '-21lnx' to each side of the equation.
-21ln + 40lnx + -21lnx = 21lnx + -21lnx

Combine like terms: 40lnx + -21lnx = 19lnx
-21ln + 19lnx = 21lnx + -21lnx

Combine like terms: 21lnx + -21lnx = 0
-21ln + 19lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 19x) = 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 '(-21 + 19x)' equal to zero and attempt to solve:

Simplifying
-21 + 19x = 0

Solving
-21 + 19x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 19x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 19x = 0 + 21
19x = 0 + 21

Combine like terms: 0 + 21 = 21
19x = 21

Add '-19x' to each side of the equation.
19x + -19x = 21 + -19x

Combine like terms: 19x + -19x = 0
0 = 21 + -19x

Simplifying
0 = 21 + -19x

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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