In(10+x)=Ln(3+4x)

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Solution for In(10+x)=Ln(3+4x) equation: 


Simplifying
In(10 + x) = Ln(3 + 4x)
(10 * nI + x * nI) = Ln(3 + 4x)
(10nI + nxI) = Ln(3 + 4x)
10nI + nxI = (3 * nL + 4x * nL)
10nI + nxI = (3nL + 4nxL)

Solving
10nI + nxI = 3nL + 4nxL

Solving for variable 'n'.

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

Add '-3nL' to each side of the equation.
10nI + -3nL + nxI = 3nL + -3nL + 4nxL

Combine like terms: 3nL + -3nL = 0
10nI + -3nL + nxI = 0 + 4nxL
10nI + -3nL + nxI = 4nxL

Add '-4nxL' to each side of the equation.
10nI + -3nL + nxI + -4nxL = 4nxL + -4nxL

Combine like terms: 4nxL + -4nxL = 0
10nI + -3nL + nxI + -4nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(10I + -3L + xI + -4xL) = 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 '(10I + -3L + xI + -4xL)' equal to zero and attempt to solve:

Simplifying
10I + -3L + xI + -4xL = 0

Solving
10I + -3L + xI + -4xL = 0

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

Add '-10I' to each side of the equation.
10I + -3L + xI + -10I + -4xL = 0 + -10I

Reorder the terms:
10I + -10I + -3L + xI + -4xL = 0 + -10I

Combine like terms: 10I + -10I = 0
0 + -3L + xI + -4xL = 0 + -10I
-3L + xI + -4xL = 0 + -10I
Remove the zero:
-3L + xI + -4xL = -10I

Add '3L' to each side of the equation.
-3L + xI + 3L + -4xL = -10I + 3L

Reorder the terms:
-3L + 3L + xI + -4xL = -10I + 3L

Combine like terms: -3L + 3L = 0
0 + xI + -4xL = -10I + 3L
xI + -4xL = -10I + 3L

Add '-1xI' to each side of the equation.
xI + -1xI + -4xL = -10I + 3L + -1xI

Combine like terms: xI + -1xI = 0
0 + -4xL = -10I + 3L + -1xI
-4xL = -10I + 3L + -1xI

Add '4xL' to each side of the equation.
-4xL + 4xL = -10I + 3L + -1xI + 4xL

Combine like terms: -4xL + 4xL = 0
0 = -10I + 3L + -1xI + 4xL

Simplifying
0 = -10I + 3L + -1xI + 4xL

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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