Ln(2x^2-15)=ln(x^2+34)

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Solution for Ln(2x^2-15)=ln(x^2+34) equation:


Simplifying
Ln(2x2 + -15) = ln(x2 + 34)

Reorder the terms:
nL(-15 + 2x2) = ln(x2 + 34)
(-15 * nL + 2x2 * nL) = ln(x2 + 34)
(-15nL + 2nx2L) = ln(x2 + 34)

Reorder the terms:
-15nL + 2nx2L = ln(34 + x2)
-15nL + 2nx2L = (34 * ln + x2 * ln)
-15nL + 2nx2L = (34ln + lnx2)

Solving
-15nL + 2nx2L = 34ln + lnx2

Solving for variable 'n'.

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

Add '-34ln' to each side of the equation.
-15nL + -34ln + 2nx2L = 34ln + -34ln + lnx2

Reorder the terms:
-34ln + -15nL + 2nx2L = 34ln + -34ln + lnx2

Combine like terms: 34ln + -34ln = 0
-34ln + -15nL + 2nx2L = 0 + lnx2
-34ln + -15nL + 2nx2L = lnx2

Add '-1lnx2' to each side of the equation.
-34ln + -15nL + -1lnx2 + 2nx2L = lnx2 + -1lnx2

Reorder the terms:
-34ln + -1lnx2 + -15nL + 2nx2L = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-34ln + -1lnx2 + -15nL + 2nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-34l + -1lx2 + -15L + 2x2L) = 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 '(-34l + -1lx2 + -15L + 2x2L)' equal to zero and attempt to solve: Simplifying -34l + -1lx2 + -15L + 2x2L = 0 Reorder the terms: -15L + -34l + -1lx2 + 2x2L = 0 Solving -15L + -34l + -1lx2 + 2x2L = 0 Move all terms containing n to the left, all other terms to the right. Add '15L' to each side of the equation. -15L + -34l + -1lx2 + 15L + 2x2L = 0 + 15L Reorder the terms: -15L + 15L + -34l + -1lx2 + 2x2L = 0 + 15L Combine like terms: -15L + 15L = 0 0 + -34l + -1lx2 + 2x2L = 0 + 15L -34l + -1lx2 + 2x2L = 0 + 15L Remove the zero: -34l + -1lx2 + 2x2L = 15L Add '34l' to each side of the equation. -34l + -1lx2 + 34l + 2x2L = 15L + 34l Reorder the terms: -34l + 34l + -1lx2 + 2x2L = 15L + 34l Combine like terms: -34l + 34l = 0 0 + -1lx2 + 2x2L = 15L + 34l -1lx2 + 2x2L = 15L + 34l Add 'lx2' to each side of the equation. -1lx2 + lx2 + 2x2L = 15L + 34l + lx2 Combine like terms: -1lx2 + lx2 = 0 0 + 2x2L = 15L + 34l + lx2 2x2L = 15L + 34l + lx2 Add '-2x2L' to each side of the equation. 2x2L + -2x2L = 15L + 34l + lx2 + -2x2L Combine like terms: 2x2L + -2x2L = 0 0 = 15L + 34l + lx2 + -2x2L Simplifying 0 = 15L + 34l + lx2 + -2x2L 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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