ln(2x-5)=ln(15)-on(x-3)

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Solution for ln(2x-5)=ln(15)-on(x-3) equation: 


Simplifying
ln(2x + -5) = ln(15) + -1on(x + -3)

Reorder the terms:
ln(-5 + 2x) = ln(15) + -1on(x + -3)
(-5 * ln + 2x * ln) = ln(15) + -1on(x + -3)
(-5ln + 2lnx) = ln(15) + -1on(x + -3)

Reorder the terms for easier multiplication:
-5ln + 2lnx = 15ln + -1on(x + -3)

Reorder the terms:
-5ln + 2lnx = 15ln + -1no(-3 + x)
-5ln + 2lnx = 15ln + (-3 * -1no + x * -1no)
-5ln + 2lnx = 15ln + (3no + -1nox)

Solving
-5ln + 2lnx = 15ln + 3no + -1nox

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
-5ln + -15ln + 2lnx = 15ln + 3no + -15ln + -1nox

Combine like terms: -5ln + -15ln = -20ln
-20ln + 2lnx = 15ln + 3no + -15ln + -1nox

Reorder the terms:
-20ln + 2lnx = 15ln + -15ln + 3no + -1nox

Combine like terms: 15ln + -15ln = 0
-20ln + 2lnx = 0 + 3no + -1nox
-20ln + 2lnx = 3no + -1nox

Reorder the terms:
-20ln + 2lnx + -3no + nox = 3no + -3no + -1nox + nox

Combine like terms: 3no + -3no = 0
-20ln + 2lnx + -3no + nox = 0 + -1nox + nox
-20ln + 2lnx + -3no + nox = -1nox + nox

Combine like terms: -1nox + nox = 0
-20ln + 2lnx + -3no + nox = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-20l + 2lx + -3o + ox) = 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 '(-20l + 2lx + -3o + ox)' equal to zero and attempt to solve:

Simplifying
-20l + 2lx + -3o + ox = 0

Solving
-20l + 2lx + -3o + ox = 0

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

Add '3o' to each side of the equation.
-20l + 2lx + -3o + 3o + ox = 0 + 3o

Combine like terms: -3o + 3o = 0
-20l + 2lx + 0 + ox = 0 + 3o
-20l + 2lx + ox = 0 + 3o
Remove the zero:
-20l + 2lx + ox = 3o

Add '-1ox' to each side of the equation.
-20l + 2lx + ox + -1ox = 3o + -1ox

Combine like terms: ox + -1ox = 0
-20l + 2lx + 0 = 3o + -1ox
-20l + 2lx = 3o + -1ox

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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