Àlgebra

ae^{x}+be^{y} = e^{ ( ln(a)+x ) [+] ( ln(b)+y ) }

ae^{x}+be^{x} = e^{ ( ln(a)+x ) [+] ( ln(b)+x ) } = e^{( ln(a) [+] ln(b) )+x} = (a+b)·e^{x}

(a+b)·e^{x} = 1

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

(a+b)·e^{x} = c

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

ln(16) = ln(8+8) = 3·ln(2) [+] 3·ln(2) = ...

... 3·ln(2)+( 0 [+] 0 ) = 3·ln(2)+( ln(1) [+] ln(1) ) = 3·ln(2)+ln(1+1) = 4·ln(2) = ln(2^{4})

ln(30) = ln(3+27) = ln(3) [+] 3·ln(3) = ...

... ln(3)+( 0 [+] 2·ln(3) ) = ln(3)+( ln(1) [+] ln(9) ) = ln(3)+ln(1+9) = ln(3)+ln(10)

ln(20) = ln(16+4) = 2·ln(4) [+] ln(4) = ...

... ln(4)+( ln(4) [+] 0 ) = ln(4)+( ln(4) [+] ln(1) ) = ln(4)+ln(4+1) = ln(4)+ln(5)

2·( ln(x) [+] ln(y) ) = 2·ln(x+y) = ln( (x+y)^{2} ) = ...

... ln(x^{2}) [+] ln(2xy) [+] ln(y^{2})

( ln(x) [+] ln(y) )+( ln(x) [+] ln(y) ) = ...

... ( ( ln(x) [+] ln(y) )+ln(x) ) [+] ( ( ln(x) [+] ln(y) )+ln(y) )

n·e^{ln(x) [+] ln(y)} = n·e^{ln(x+y)} = nx+ny = ne^{ln(x)}+ne^{ln(y)}

x^{n}+x^{m} = c

x = c^{( 1/( n [+] m ) )}

x^{n}+x^{m} = ( c^{( 1/( n [+] m ) )} )^{n}+( c^{( 1/( n [+] m ) )} )^{m} = ...

... ( c^{( 1/( n [+] m ) )} )^{( n [+] m )} = c^{( ( n [+] m )/( n [+] m ) )} = c

d_{x}[y(x)]^{n}+d_{x}[y(x)]^{m} = d_{x}[f(x)]

x = ( f(x) )^{[o(x)o]( 1/( n [+] m ) )}

ax^{n}+bx^{m} = c

polinomi asociat resoluble:

px^{n}+qx^{m} = c

p = a^{( 1/( ( log_{c}(a)+n ) [+] ( log_{c}(b)+m ) ) )}

q = b^{( 1/( ( log_{c}(a)+n ) [+] ( log_{c}(b)+m ) ) )}

x = c^{( 1/( ( log_{c}(a)+n ) [+] ( log_{c}(b)+m ) ) )}

px^{n}+qx^{m} = ...

... ( c^{( 1/( ( log_{c}(a)+n ) [+] ( log_{c}(b)+m ) ) )} )^{( log_{c}(a)+n )}+...

... ( c^{( 1/( ( log_{c}(a)+n ) [+] ( log_{c}(b)+m ) ) )} )^{( log_{c}(b)+m )} = c

100·x^{100}+1000·x^{48} = 10

polinomi asociat resoluble:

px^{100}+qx^{48} = 10

p = 10^{( 2/( 102 [+] 51 ) )}

q = 10^{( 3/( 102 [+] 51 ) )}

x = 10^{( 1/( 102 [+] 51 ) )}

81·x^{8}+27·x^{3} = 3

polinomi asociat resoluble:

px^{8}+qx^{3} = 3

p = 3^{( 4/( 12 [+] 6 ) )}

q = 3^{( 3/( 12 [+] 6 ) )}

x = 3^{( 1/( 12 [+] 6 ) )}