ln(4x^2)+ln(e)-ln(3x)=1

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Solution for ln(4x^2)+ln(e)-ln(3x)=1 equation:


Simplifying
ln(4x2) + ln(e) + -1ln(3x) = 1

Remove parenthesis around (4x2)
ln * 4x2 + ln(e) + -1ln(3x) = 1

Reorder the terms for easier multiplication:
4ln * x2 + ln(e) + -1ln(3x) = 1

Multiply ln * x2
4lnx2 + ln(e) + -1ln(3x) = 1

Multiply ln * e
4lnx2 + eln + -1ln(3x) = 1

Remove parenthesis around (3x)
4lnx2 + eln + -1ln * 3x = 1

Reorder the terms for easier multiplication:
4lnx2 + eln + -1 * 3ln * x = 1

Multiply -1 * 3
4lnx2 + eln + -3ln * x = 1

Multiply ln * x
4lnx2 + eln + -3lnx = 1

Reorder the terms:
eln + -3lnx + 4lnx2 = 1

Solving
eln + -3lnx + 4lnx2 = 1

Solving for variable 'e'.

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

Add '3lnx' to each side of the equation.
eln + -3lnx + 3lnx + 4lnx2 = 1 + 3lnx

Combine like terms: -3lnx + 3lnx = 0
eln + 0 + 4lnx2 = 1 + 3lnx
eln + 4lnx2 = 1 + 3lnx

Add '-4lnx2' to each side of the equation.
eln + 4lnx2 + -4lnx2 = 1 + 3lnx + -4lnx2

Combine like terms: 4lnx2 + -4lnx2 = 0
eln + 0 = 1 + 3lnx + -4lnx2
eln = 1 + 3lnx + -4lnx2

Divide each side by 'ln'.
e = l-1n-1 + 3x + -4x2

Simplifying
e = l-1n-1 + 3x + -4x2

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