ln(7x+1)=ln(x^2+1)

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Solution for ln(7x+1)=ln(x^2+1) equation: 


Simplifying
ln(7x + 1) = ln(x2 + 1)

Reorder the terms:
ln(1 + 7x) = ln(x2 + 1)
(1 * ln + 7x * ln) = ln(x2 + 1)
(1ln + 7lnx) = ln(x2 + 1)

Reorder the terms:
1ln + 7lnx = ln(1 + x2)
1ln + 7lnx = (1 * ln + x2 * ln)
1ln + 7lnx = (1ln + lnx2)

Add '-1ln' to each side of the equation.
1ln + -1ln + 7lnx = 1ln + -1ln + lnx2

Combine like terms: 1ln + -1ln = 0
0 + 7lnx = 1ln + -1ln + lnx2
7lnx = 1ln + -1ln + lnx2

Combine like terms: 1ln + -1ln = 0
7lnx = 0 + lnx2
7lnx = lnx2

Solving
7lnx = lnx2

Solving for variable 'l'.

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

Add '-1lnx2' to each side of the equation.
7lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
7lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(7 + -1x) = 0


Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve:

Simplifying
lnx = 0

Solving
lnx = 0

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

Simplifying
lnx = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Add 'x' to each side of the equation.
-1x + x = -7 + x

Combine like terms: -1x + x = 0
0 = -7 + x

Simplifying
0 = -7 + 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.

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