ln(4x)+ln(x)=ln(16)

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Solution for ln(4x)+ln(x)=ln(16) equation: 


Simplifying
ln(4x) + ln(x) = ln(16)

Remove parenthesis around (4x)
ln * 4x + ln(x) = ln(16)

Reorder the terms for easier multiplication:
4ln * x + ln(x) = ln(16)

Multiply ln * x
4lnx + ln(x) = ln(16)

Multiply ln * x
4lnx + lnx = ln(16)

Combine like terms: 4lnx + lnx = 5lnx
5lnx = ln(16)

Reorder the terms for easier multiplication:
5lnx = 16ln

Solving
5lnx = 16ln

Solving for variable 'l'.

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

Add '-16ln' to each side of the equation.
-16ln + 5lnx = 16ln + -16ln

Combine like terms: 16ln + -16ln = 0
-16ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-16 + 5x) = 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 '(-16 + 5x)' equal to zero and attempt to solve:

Simplifying
-16 + 5x = 0

Solving
-16 + 5x = 0

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

Add '16' to each side of the equation.
-16 + 16 + 5x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 5x = 0 + 16
5x = 0 + 16

Combine like terms: 0 + 16 = 16
5x = 16

Add '-5x' to each side of the equation.
5x + -5x = 16 + -5x

Combine like terms: 5x + -5x = 0
0 = 16 + -5x

Simplifying
0 = 16 + -5x

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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