álgebra

c^{log_{c^{n}}(c)} = c^{(1/n)}

log_{c^{n}}(c) = log_{c}(c^{(1/n)}) = (1/n)

c = (c^{n})^{(1/n)}

n[+]m = ( (n+m)/(1+1) ) = ((n+m)/2)

n[+]0 = (n/2)

x^{n}[·]x^{m} = x^{((n+m)/2)}

x^{n}[·]1 = x^{(n/2)}

m[+]...(n)...[+]m = m·( 1[+]...(n)...[+]1 ) = m

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

a[·]b = x^{log_{x}(a)}[·]x^{log_{x}(b)} = x^{( (log_{x}(ab))/2 )} = (ab)^{(1/2)}

a[·]( p+q ) = x^{log_{x}(a)}[·]x^{log_{x}( p+q )} = ( ap+aq )^{(1/2)}

a[·]( p[+] q) = x^{log_{x}(a)}[·]x^{log_{x}( p[+]q )} = ( ap[+]aq )^{(1/2)}

( ca·x^{n} )^{(1/2)}+( cb·x^{m} )^{(1/2)} = c

(ca)[·]x^{n}+(cb)[·]x^{m} = c

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

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

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

( 2x^{3} )^{(1/2)}+( 4x^{2} )^{(1/2)} = 2

2[·]x^{3}+4[·]x^{2} = 2

x = 2^{( 1/( ( 4 ) [[+]] ( 4 ) ) )}

( 3x^{7} )^{(1/2)}+( 9x^{6} )^{(1/2)} = 3

3[·]x^{7}+9[·]x^{6} = 3

x = 3^{( 1/( ( 8 ) [[+]] ( 8 ) ) )}