ln(15x)=ln(x^2+56)

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Solution for ln(15x)=ln(x^2+56) equation:


Simplifying
ln(15x) = ln(x2 + 56)

Remove parenthesis around (15x)
ln * 15x = ln(x2 + 56)

Reorder the terms for easier multiplication:
15ln * x = ln(x2 + 56)

Multiply ln * x
15lnx = ln(x2 + 56)

Reorder the terms:
15lnx = ln(56 + x2)
15lnx = (56 * ln + x2 * ln)
15lnx = (56ln + lnx2)

Solving
15lnx = 56ln + lnx2

Solving for variable 'l'.

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

Add '-56ln' to each side of the equation.
-56ln + 15lnx = 56ln + -56ln + lnx2

Combine like terms: 56ln + -56ln = 0
-56ln + 15lnx = 0 + lnx2
-56ln + 15lnx = lnx2

Add '-1lnx2' to each side of the equation.
-56ln + 15lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-56ln + 15lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-56 + 15x + -1x2) = 0

Factor a trinomial.
ln((-8 + x)(7 + -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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -1x 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 '(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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