2ln(z)+5ln(2)=ln(z)-ln(4)

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Solution for 2ln(z)+5ln(2)=ln(z)-ln(4) equation:


Simplifying
2ln(z) + 5ln(2) = ln(z) + -1ln(4)

Multiply ln * z
2lnz + 5ln(2) = ln(z) + -1ln(4)

Reorder the terms for easier multiplication:
2lnz + 5 * 2ln = ln(z) + -1ln(4)

Multiply 5 * 2
2lnz + 10ln = ln(z) + -1ln(4)

Reorder the terms:
10ln + 2lnz = ln(z) + -1ln(4)

Multiply ln * z
10ln + 2lnz = lnz + -1ln(4)

Reorder the terms for easier multiplication:
10ln + 2lnz = lnz + -1 * 4ln

Multiply -1 * 4
10ln + 2lnz = lnz + -4ln

Reorder the terms:
10ln + 2lnz = -4ln + lnz

Solving
10ln + 2lnz = -4ln + lnz

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
10ln + 4ln + 2lnz = -4ln + 4ln + lnz

Combine like terms: 10ln + 4ln = 14ln
14ln + 2lnz = -4ln + 4ln + lnz

Combine like terms: -4ln + 4ln = 0
14ln + 2lnz = 0 + lnz
14ln + 2lnz = lnz

Add '-1lnz' to each side of the equation.
14ln + 2lnz + -1lnz = lnz + -1lnz

Combine like terms: 2lnz + -1lnz = 1lnz
14ln + 1lnz = lnz + -1lnz

Combine like terms: lnz + -1lnz = 0
14ln + 1lnz = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(14 + z) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(14 + z)' equal to zero and attempt to solve: Simplifying 14 + z = 0 Solving 14 + z = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + z = 0 + -14 z = 0 + -14 Combine like terms: 0 + -14 = -14 z = -14 Add '-1z' to each side of the equation. z + -1z = -14 + -1z Combine like terms: z + -1z = 0 0 = -14 + -1z Simplifying 0 = -14 + -1z 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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