lm(7x-4)=ln(2x+11)

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Solution for lm(7x-4)=ln(2x+11) equation:


Simplifying
lm(7x + -4) = ln(2x + 11)

Reorder the terms:
lm(-4 + 7x) = ln(2x + 11)
(-4 * lm + 7x * lm) = ln(2x + 11)
(-4lm + 7lmx) = ln(2x + 11)

Reorder the terms:
-4lm + 7lmx = ln(11 + 2x)
-4lm + 7lmx = (11 * ln + 2x * ln)
-4lm + 7lmx = (11ln + 2lnx)

Solving
-4lm + 7lmx = 11ln + 2lnx

Solving for variable 'l'.

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

Add '-11ln' to each side of the equation.
-4lm + 7lmx + -11ln = 11ln + -11ln + 2lnx

Combine like terms: 11ln + -11ln = 0
-4lm + 7lmx + -11ln = 0 + 2lnx
-4lm + 7lmx + -11ln = 2lnx

Add '-2lnx' to each side of the equation.
-4lm + 7lmx + -11ln + -2lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-4lm + 7lmx + -11ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'l'.
l(-4m + 7mx + -11n + -2nx) = 0

Subproblem 1

Set the factor 'l' equal to zero and attempt to solve: Simplifying l = 0 Solving l = 0 Move all terms containing l to the left, all other terms to the right. Simplifying l = 0

Subproblem 2

Set the factor '(-4m + 7mx + -11n + -2nx)' equal to zero and attempt to solve: Simplifying -4m + 7mx + -11n + -2nx = 0 Solving -4m + 7mx + -11n + -2nx = 0 Move all terms containing l to the left, all other terms to the right. Add '4m' to each side of the equation. -4m + 7mx + -11n + 4m + -2nx = 0 + 4m Reorder the terms: -4m + 4m + 7mx + -11n + -2nx = 0 + 4m Combine like terms: -4m + 4m = 0 0 + 7mx + -11n + -2nx = 0 + 4m 7mx + -11n + -2nx = 0 + 4m Remove the zero: 7mx + -11n + -2nx = 4m Add '-7mx' to each side of the equation. 7mx + -11n + -7mx + -2nx = 4m + -7mx Reorder the terms: 7mx + -7mx + -11n + -2nx = 4m + -7mx Combine like terms: 7mx + -7mx = 0 0 + -11n + -2nx = 4m + -7mx -11n + -2nx = 4m + -7mx Add '11n' to each side of the equation. -11n + 11n + -2nx = 4m + -7mx + 11n Combine like terms: -11n + 11n = 0 0 + -2nx = 4m + -7mx + 11n -2nx = 4m + -7mx + 11n Add '2nx' to each side of the equation. -2nx + 2nx = 4m + -7mx + 11n + 2nx Combine like terms: -2nx + 2nx = 0 0 = 4m + -7mx + 11n + 2nx Simplifying 0 = 4m + -7mx + 11n + 2nx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

l = {0}

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