ln(7+2X)=In(1+4x)

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Solution for ln(7+2X)=In(1+4x) equation: 


Simplifying
ln(7 + 2X) = In(1 + 4x)
(7 * ln + 2X * ln) = In(1 + 4x)
(7ln + 2lnX) = In(1 + 4x)
7ln + 2lnX = (1 * nI + 4x * nI)
7ln + 2lnX = (1nI + 4nxI)

Solving
7ln + 2lnX = 1nI + 4nxI

Solving for variable 'l'.

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

Reorder the terms:
7ln + 2lnX + -1nI + -4nxI = 1nI + -1nI + 4nxI + -4nxI

Combine like terms: 1nI + -1nI = 0
7ln + 2lnX + -1nI + -4nxI = 0 + 4nxI + -4nxI
7ln + 2lnX + -1nI + -4nxI = 4nxI + -4nxI

Combine like terms: 4nxI + -4nxI = 0
7ln + 2lnX + -1nI + -4nxI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(7l + 2lX + -1I + -4xI) = 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 '(7l + 2lX + -1I + -4xI)' equal to zero and attempt to solve:

Simplifying
7l + 2lX + -1I + -4xI = 0

Reorder the terms:
-1I + 7l + 2lX + -4xI = 0

Solving
-1I + 7l + 2lX + -4xI = 0

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

Add 'I' to each side of the equation.
-1I + 7l + 2lX + I + -4xI = 0 + I

Reorder the terms:
-1I + I + 7l + 2lX + -4xI = 0 + I

Combine like terms: -1I + I = 0
0 + 7l + 2lX + -4xI = 0 + I
7l + 2lX + -4xI = 0 + I
Remove the zero:
7l + 2lX + -4xI = I

Add '4xI' to each side of the equation.
7l + 2lX + -4xI + 4xI = I + 4xI

Combine like terms: -4xI + 4xI = 0
7l + 2lX + 0 = I + 4xI
7l + 2lX = I + 4xI

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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