logaritme suma

ln(a+b) = ln( e^{ln(a)}+e^{ln(b)} ) = [ln(a)+(-1)·ln(b)]+ln(b)


ln(a+a) = [ln(a)+(-1)·ln(a)]+ln(a)
ln(a+a) = ln(2)+ln(a)


ln(a+b+c) = [ ln(a)+(-1)( [ln(b)+(-1)·ln(c)]+ln(c) )]+[ln(b)+(-1)·ln(c)]+ln(c)


ln(a+a+a) = [ ln(a)+(-1)( [ln(a)+(-1)·ln(a)]+ln(a) )]+[ln(a)+(-1)·ln(a)]+ln(a)
ln(a+a+a) = ln(3/2)+ln(2)+ln(a)


ln( x^{p}+y^{q} ) = z  <==> ...
... z = [ ln(p!)+e[( 1/p! )]+(-1)( ln(q!)+e[( 1/q! )] ) ]+( ln(q!)+e[( 1/q! )] ) ...
... x = e[( 1/p! )] ...
... y = e[( 1/q! )]


ln( x^{p}+y^{q} ) = z^{n}  <==> ...
... z = ( [ ln(p!)+e[( 1/p! )]+(-1)( ln(q!)+e[( 1/q! )] ) ]+( ln(q!)+e[( 1/q! )] ) )^{(1/n)} ...
... x = e[( 1/p! )] ...
... y = e[( 1/q! )]


ln( ax^{p}+by^{q} ) = cz^{n}  <==> ...
... ax^{p}+by^{q} = e^{cz^{n}}  <==> ...
... z = ( (1/c)·( [ ln(a·p!)+e[( 1/p! )]+(-1)( ln(b·q!)+e[( 1/q! )] ) ]+( ln(b·q!)+e[( 1/q! )] ) ) )^{(1/n)} ...
... x = e[( 1/p! )] ...
... y = e[( 1/q! )]


ln( ax^{p}+by^{q} ) = ln(c)+z^{n}  <==> ...
... ax^{p}+by^{q} = c·e^{z^{n}}  <==> ...
... z = ( (-1)·ln(c)+[ ln(a·p!)+e[( 1/p! )]+(-1)( ln(b·q!)+e[( 1/q! )] ) ]+( ln(b·q!)+e[( 1/q! )] ) )^{(1/n)} ...
... x = e[( 1/p! )] ...
... y = e[( 1/q! )]


ln( ax^{p}+by^{q} ) = ln(s)+cz^{n}  <==> ...
... ax^{p}+by^{q} = s·e^{cz^{n}}  <==> ...
... z = ( (1/c)·( (-1)·ln(s)+[ ln(a·p!)+e[( 1/p! )]+(-1)( ln(b·q!)+e[( 1/q! )] ) ]+( ln(b·q!)+e[( 1/q! )] ) ) )^{(1/n)}
... x = e[( 1/p! )] ...
... y = e[( 1/q! )]