Ln(2x+9)-sqrtln(5x-3)=0

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Solution for Ln(2x+9)-sqrtln(5x-3)=0 equation:


Simplifying
Ln(2x + 9) + -1sqrtln(5x + -3) = 0

Reorder the terms:
nL(9 + 2x) + -1sqrtln(5x + -3) = 0
(9 * nL + 2x * nL) + -1sqrtln(5x + -3) = 0
(9nL + 2nxL) + -1sqrtln(5x + -3) = 0

Reorder the terms:
9nL + 2nxL + -1lnqrst(-3 + 5x) = 0
9nL + 2nxL + (-3 * -1lnqrst + 5x * -1lnqrst) = 0
9nL + 2nxL + (3lnqrst + -5lnqrstx) = 0

Reorder the terms:
3lnqrst + -5lnqrstx + 9nL + 2nxL = 0

Solving
3lnqrst + -5lnqrstx + 9nL + 2nxL = 0

Solving for variable 'l'.

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

Add '-9nL' to each side of the equation.
3lnqrst + -5lnqrstx + 9nL + -9nL + 2nxL = 0 + -9nL

Combine like terms: 9nL + -9nL = 0
3lnqrst + -5lnqrstx + 0 + 2nxL = 0 + -9nL
3lnqrst + -5lnqrstx + 2nxL = 0 + -9nL
Remove the zero:
3lnqrst + -5lnqrstx + 2nxL = -9nL

Add '-2nxL' to each side of the equation.
3lnqrst + -5lnqrstx + 2nxL + -2nxL = -9nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
3lnqrst + -5lnqrstx + 0 = -9nL + -2nxL
3lnqrst + -5lnqrstx = -9nL + -2nxL

Reorder the terms:
3lnqrst + -5lnqrstx + 9nL + 2nxL = -9nL + 9nL + -2nxL + 2nxL

Combine like terms: -9nL + 9nL = 0
3lnqrst + -5lnqrstx + 9nL + 2nxL = 0 + -2nxL + 2nxL
3lnqrst + -5lnqrstx + 9nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
3lnqrst + -5lnqrstx + 9nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3lqrst + -5lqrstx + 9L + 2xL) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(3lqrst + -5lqrstx + 9L + 2xL)' equal to zero and attempt to solve: Simplifying 3lqrst + -5lqrstx + 9L + 2xL = 0 Reorder the terms: 9L + 3lqrst + -5lqrstx + 2xL = 0 Solving 9L + 3lqrst + -5lqrstx + 2xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-9L' to each side of the equation. 9L + 3lqrst + -5lqrstx + -9L + 2xL = 0 + -9L Reorder the terms: 9L + -9L + 3lqrst + -5lqrstx + 2xL = 0 + -9L Combine like terms: 9L + -9L = 0 0 + 3lqrst + -5lqrstx + 2xL = 0 + -9L 3lqrst + -5lqrstx + 2xL = 0 + -9L Remove the zero: 3lqrst + -5lqrstx + 2xL = -9L Add '-2xL' to each side of the equation. 3lqrst + -5lqrstx + 2xL + -2xL = -9L + -2xL Combine like terms: 2xL + -2xL = 0 3lqrst + -5lqrstx + 0 = -9L + -2xL 3lqrst + -5lqrstx = -9L + -2xL 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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