8*ln(14)ln(7x)=8*ln(2)

Solution for 8*ln(14)ln(7x)=8*ln(2) equation:

Simplifying
8ln(14) * ln(7x) = 8ln(2)

Remove parenthesis around (7x)
8ln * 14ln * 7x = 8ln(2)

Reorder the terms for easier multiplication:
8 * 14 * 7ln * ln * x = 8ln(2)

Multiply 8 * 14
112 * 7ln * ln * x = 8ln(2)

Multiply 112 * 7
784ln * ln * x = 8ln(2)

Multiply ln * ln
784l2n2 * x = 8ln(2)

Multiply l2n2 * x
784l2n2x = 8ln(2)

Reorder the terms for easier multiplication:
784l2n2x = 8 * 2ln

Multiply 8 * 2
784l2n2x = 16ln

Solving
784l2n2x = 16ln

Solving for variable 'l'.

Reorder the terms:
-16ln + 784l2n2x = 16ln + -16ln

Combine like terms: 16ln + -16ln = 0
-16ln + 784l2n2x = 0

Factor out the Greatest Common Factor (GCF), '16ln'.
16ln(-1 + 49lnx) = 0

Ignore the factor 16.
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 + 49lnx)' equal to zero and attempt to solve:

Simplifying
-1 + 49lnx = 0

Solving
-1 + 49lnx = 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 + 49lnx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 49lnx = 0 + 1
49lnx = 0 + 1

Combine like terms: 0 + 1 = 1
49lnx = 1

Divide each side by '49nx'.
l = 0.02040816327n-1x-1

Simplifying
l = 0.02040816327n-1x-1
Solution
l = {0.02040816327n-1x-1}