[tex]49^x-(7*5)^x-25^x=0[/tex]
[tex]49^x-7^x*5^x-25^x=0[/tex]
impartim relatia prin [tex]25^x[/tex]
[tex] \frac{49^x}{25^x}- \frac{7^x*5^x}{25^x} -\frac{25^x}{25^x}=0 [/tex]
[tex] [(\frac{7}{5})^2]^x- \frac{7^x*5^x}{(5^2)^x}-1=0 [/tex]
[tex] [(\frac{7}{5})^x]^2-( \frac{7}{5})^x-1=0[/tex]
Notam [tex] (\frac{7}{5})^x [/tex]=y, y>0;
y²-y-1=0
Δ=(-1)²-(-1)*4=5
y₁=[tex] \frac{1- \sqrt{5} }{2} [/tex] <0 care nu ne convine
y₂=[tex] \frac{1+ \sqrt{5} }{2} [/tex]
[tex] (\frac{7}{5})^x= \frac{1+ \sqrt{5} }{2} [/tex]
[tex]x=log _{ \frac{7}{5} }( \frac{1+ \sqrt{5} }{2} ) [/tex]
