ln(8x-3)-lnx=ln(7)

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Solution for ln(8x-3)-lnx=ln(7) equation:


Simplifying
ln(8x + -3) + -1lnx = ln(7)

Reorder the terms:
ln(-3 + 8x) + -1lnx = ln(7)
(-3 * ln + 8x * ln) + -1lnx = ln(7)
(-3ln + 8lnx) + -1lnx = ln(7)

Combine like terms: 8lnx + -1lnx = 7lnx
-3ln + 7lnx = ln(7)

Reorder the terms for easier multiplication:
-3ln + 7lnx = 7ln

Solving
-3ln + 7lnx = 7ln

Solving for variable 'l'.

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

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

Combine like terms: -3ln + -7ln = -10ln
-10ln + 7lnx = 7ln + -7ln

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-10 + 7x) = 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 '(-10 + 7x)' equal to zero and attempt to solve: Simplifying -10 + 7x = 0 Solving -10 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 7x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7x = 0 + 10 7x = 0 + 10 Combine like terms: 0 + 10 = 10 7x = 10 Add '-7x' to each side of the equation. 7x + -7x = 10 + -7x Combine like terms: 7x + -7x = 0 0 = 10 + -7x Simplifying 0 = 10 + -7x 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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