ln(3x+1)+ln(ax+7)=y

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Solution for ln(3x+1)+ln(ax+7)=y equation: 


Simplifying
ln(3x + 1) + ln(ax + 7) = y

Reorder the terms:
ln(1 + 3x) + ln(ax + 7) = y
(1 * ln + 3x * ln) + ln(ax + 7) = y
(1ln + 3lnx) + ln(ax + 7) = y

Reorder the terms:
1ln + 3lnx + ln(7 + ax) = y
1ln + 3lnx + (7 * ln + ax * ln) = y

Reorder the terms:
1ln + 3lnx + (alnx + 7ln) = y
1ln + 3lnx + (alnx + 7ln) = y

Reorder the terms:
alnx + 1ln + 7ln + 3lnx = y

Combine like terms: 1ln + 7ln = 8ln
alnx + 8ln + 3lnx = y

Solving
alnx + 8ln + 3lnx = y

Solving for variable 'a'.

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

Add '-8ln' to each side of the equation.
alnx + 8ln + -8ln + 3lnx = -8ln + y

Combine like terms: 8ln + -8ln = 0
alnx + 0 + 3lnx = -8ln + y
alnx + 3lnx = -8ln + y

Add '-3lnx' to each side of the equation.
alnx + 3lnx + -3lnx = -8ln + -3lnx + y

Combine like terms: 3lnx + -3lnx = 0
alnx + 0 = -8ln + -3lnx + y
alnx = -8ln + -3lnx + y

Divide each side by 'lnx'.
a = -8x-1 + -3 + l-1n-1x-1y

Simplifying
a = -8x-1 + -3 + l-1n-1x-1y

Reorder the terms:
a = -3 + l-1n-1x-1y + -8x-1

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