Ln(e+5)-Ln(x-2)=1

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Solution for Ln(e+5)-Ln(x-2)=1 equation: 


Simplifying
Ln(e + 5) + -1Ln(x + -2) = 1

Reorder the terms:
nL(5 + e) + -1Ln(x + -2) = 1
(5 * nL + e * nL) + -1Ln(x + -2) = 1

Reorder the terms:
(enL + 5nL) + -1Ln(x + -2) = 1
(enL + 5nL) + -1Ln(x + -2) = 1

Reorder the terms:
enL + 5nL + -1nL(-2 + x) = 1
enL + 5nL + (-2 * -1nL + x * -1nL) = 1
enL + 5nL + (2nL + -1nxL) = 1

Combine like terms: 5nL + 2nL = 7nL
enL + 7nL + -1nxL = 1

Solving
enL + 7nL + -1nxL = 1

Solving for variable 'e'.

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

Add '-7nL' to each side of the equation.
enL + 7nL + -7nL + -1nxL = 1 + -7nL

Combine like terms: 7nL + -7nL = 0
enL + 0 + -1nxL = 1 + -7nL
enL + -1nxL = 1 + -7nL

Add 'nxL' to each side of the equation.
enL + -1nxL + nxL = 1 + -7nL + nxL

Combine like terms: -1nxL + nxL = 0
enL + 0 = 1 + -7nL + nxL
enL = 1 + -7nL + nxL

Divide each side by 'nL'.
e = n-1L-1 + -7 + x

Simplifying
e = n-1L-1 + -7 + x

Reorder the terms:
e = -7 + n-1L-1 + x

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