Ln(8x^3)=(3)ln(8)+ln(x)

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Solution for Ln(8x^3)=(3)ln(8)+ln(x) equation: 


Simplifying
Ln(8x3) = (3) * ln(8) + ln(x)

Remove parenthesis around (8x3)
nL * 8x3 = (3) * ln(8) + ln(x)

Reorder the terms for easier multiplication:
8nL * x3 = (3) * ln(8) + ln(x)

Multiply nL * x3
8nx3L = (3) * ln(8) + ln(x)

Reorder the terms for easier multiplication:
8nx3L = 3 * 8ln + ln(x)

Multiply 3 * 8
8nx3L = 24ln + ln(x)

Multiply ln * x
8nx3L = 24ln + lnx

Solving
8nx3L = 24ln + lnx

Solving for variable 'n'.

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

Add '-24ln' to each side of the equation.
-24ln + 8nx3L = 24ln + -24ln + lnx

Combine like terms: 24ln + -24ln = 0
-24ln + 8nx3L = 0 + lnx
-24ln + 8nx3L = lnx

Add '-1lnx' to each side of the equation.
-24ln + -1lnx + 8nx3L = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-24ln + -1lnx + 8nx3L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-24l + -1lx + 8x3L) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-24l + -1lx + 8x3L)' equal to zero and attempt to solve:

Simplifying
-24l + -1lx + 8x3L = 0

Solving
-24l + -1lx + 8x3L = 0

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

Add '24l' to each side of the equation.
-24l + -1lx + 24l + 8x3L = 0 + 24l

Reorder the terms:
-24l + 24l + -1lx + 8x3L = 0 + 24l

Combine like terms: -24l + 24l = 0
0 + -1lx + 8x3L = 0 + 24l
-1lx + 8x3L = 0 + 24l
Remove the zero:
-1lx + 8x3L = 24l

Add 'lx' to each side of the equation.
-1lx + lx + 8x3L = 24l + lx

Combine like terms: -1lx + lx = 0
0 + 8x3L = 24l + lx
8x3L = 24l + lx

Add '-8x3L' to each side of the equation.
8x3L + -8x3L = 24l + lx + -8x3L

Combine like terms: 8x3L + -8x3L = 0
0 = 24l + lx + -8x3L

Simplifying
0 = 24l + lx + -8x3L

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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