Ln(8x)-2ln(2x)=ln(x)

Solution for Ln(8x)-2ln(2x)=ln(x) equation:

Simplifying
Ln(8x) + -2ln(2x) = ln(x)

Remove parenthesis around (8x)
nL * 8x + -2ln(2x) = ln(x)

Reorder the terms for easier multiplication:
8nL * x + -2ln(2x) = ln(x)

Multiply nL * x
8nxL + -2ln(2x) = ln(x)

Remove parenthesis around (2x)
8nxL + -2ln * 2x = ln(x)

Reorder the terms for easier multiplication:
8nxL + -2 * 2ln * x = ln(x)

Multiply -2 * 2
8nxL + -4ln * x = ln(x)

Multiply ln * x
8nxL + -4lnx = ln(x)

Reorder the terms:
-4lnx + 8nxL = ln(x)

Multiply ln * x
-4lnx + 8nxL = lnx

Solving
-4lnx + 8nxL = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-4lnx + -1lnx + 8nxL = lnx + -1lnx

Combine like terms: -4lnx + -1lnx = -5lnx
-5lnx + 8nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-5lnx + 8nxL = 0

Add '-8nxL' to each side of the equation.
-5lnx + 8nxL + -8nxL = 0 + -8nxL

Combine like terms: 8nxL + -8nxL = 0
-5lnx + 0 = 0 + -8nxL
-5lnx = 0 + -8nxL
Remove the zero:
-5lnx = -8nxL

Divide each side by '-5nx'.
l = 1.6L

Simplifying
l = 1.6L