Ln(x)+Ln(3x-1)=Ln(10)

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Solution for Ln(x)+Ln(3x-1)=Ln(10) equation: 


Simplifying
Ln(x) + Ln(3x + -1) = Ln(10)

Multiply nL * x
nxL + Ln(3x + -1) = Ln(10)

Reorder the terms:
nxL + nL(-1 + 3x) = Ln(10)
nxL + (-1 * nL + 3x * nL) = Ln(10)
nxL + (-1nL + 3nxL) = Ln(10)

Reorder the terms:
-1nL + nxL + 3nxL = Ln(10)

Combine like terms: nxL + 3nxL = 4nxL
-1nL + 4nxL = Ln(10)

Reorder the terms for easier multiplication:
-1nL + 4nxL = 10nL

Solving
-1nL + 4nxL = 10nL

Solving for variable 'n'.

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

Add '-10nL' to each side of the equation.
-1nL + -10nL + 4nxL = 10nL + -10nL

Combine like terms: -1nL + -10nL = -11nL
-11nL + 4nxL = 10nL + -10nL

Combine like terms: 10nL + -10nL = 0
-11nL + 4nxL = 0

Factor out the Greatest Common Factor (GCF), 'nL'.
nL(-11 + 4x) = 0


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

Simplifying
nL = 0

Solving
nL = 0

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

Simplifying
nL = 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 '(-11 + 4x)' equal to zero and attempt to solve:

Simplifying
-11 + 4x = 0

Solving
-11 + 4x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 4x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4x = 0 + 11
4x = 0 + 11

Combine like terms: 0 + 11 = 11
4x = 11

Add '-4x' to each side of the equation.
4x + -4x = 11 + -4x

Combine like terms: 4x + -4x = 0
0 = 11 + -4x

Simplifying
0 = 11 + -4x

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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