ln(30x-7)=ln(8)

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Solution for ln(30x-7)=ln(8) equation: 


Simplifying
ln(30x + -7) = ln(8)

Reorder the terms:
ln(-7 + 30x) = ln(8)
(-7 * ln + 30x * ln) = ln(8)
(-7ln + 30lnx) = ln(8)

Reorder the terms for easier multiplication:
-7ln + 30lnx = 8ln

Solving
-7ln + 30lnx = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-7ln + -8ln + 30lnx = 8ln + -8ln

Combine like terms: -7ln + -8ln = -15ln
-15ln + 30lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-15ln + 30lnx = 0

Factor out the Greatest Common Factor (GCF), '15ln'.
15ln(-1 + 2x) = 0

Ignore the factor 15.

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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Add '-2x' to each side of the equation.
2x + -2x = 1 + -2x

Combine like terms: 2x + -2x = 0
0 = 1 + -2x

Simplifying
0 = 1 + -2x

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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