ln(7x)=ln(x^2+10)

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Solution for ln(7x)=ln(x^2+10) equation:


Simplifying
ln(7x) = ln(x2 + 10)

Remove parenthesis around (7x)
ln * 7x = ln(x2 + 10)

Reorder the terms for easier multiplication:
7ln * x = ln(x2 + 10)

Multiply ln * x
7lnx = ln(x2 + 10)

Reorder the terms:
7lnx = ln(10 + x2)
7lnx = (10 * ln + x2 * ln)
7lnx = (10ln + lnx2)

Solving
7lnx = 10ln + lnx2

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-10ln + 7lnx = 10ln + -10ln + lnx2

Combine like terms: 10ln + -10ln = 0
-10ln + 7lnx = 0 + lnx2
-10ln + 7lnx = lnx2

Add '-1lnx2' to each side of the equation.
-10ln + 7lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-10ln + 7lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-10 + 7x + -1x2) = 0

Factor a trinomial.
ln((-5 + x)(2 + -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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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