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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