ln(x^2+15)=ln(7x+3)

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Solution for ln(x^2+15)=ln(7x+3) equation:


Simplifying
ln(x2 + 15) = ln(7x + 3)

Reorder the terms:
ln(15 + x2) = ln(7x + 3)
(15 * ln + x2 * ln) = ln(7x + 3)
(15ln + lnx2) = ln(7x + 3)

Reorder the terms:
15ln + lnx2 = ln(3 + 7x)
15ln + lnx2 = (3 * ln + 7x * ln)
15ln + lnx2 = (3ln + 7lnx)

Solving
15ln + lnx2 = 3ln + 7lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
15ln + -3ln + lnx2 = 3ln + -3ln + 7lnx

Combine like terms: 15ln + -3ln = 12ln
12ln + lnx2 = 3ln + -3ln + 7lnx

Combine like terms: 3ln + -3ln = 0
12ln + lnx2 = 0 + 7lnx
12ln + lnx2 = 7lnx

Add '-7lnx' to each side of the equation.
12ln + -7lnx + lnx2 = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
12ln + -7lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(12 + -7x + x2) = 0

Factor a trinomial.
ln((3 + -1x)(4 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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