Question

cum rezolv si eu ecuatia asta exponentiala ? 0,25 la puterea 5-x = 2 la puterea x+3 

Answer 1

$(\frac{1}4} )^{5-x} = 2^{x+3}$

-logaritmezi in baza e;
-exponentul iese in fata;

$(5-x)*ln(1/4)=(x+3)*ln(2)$

*ln(a/b)=ln a - ln b;

$(5-x)ln(1)-(5-x)ln2^{2} =(x+3)*ln(2)$

ln(1)=0;

$-2(5-x)ln(2)=(x+3)ln(2)$  

-impartim cu ln 2

$-10+2x=x+3$
$x=13$

verificare:

[tex](\frac{1}{4} )^{-8} =2^{16} [/tex]

[tex]({2^{-2}})^{-8}=2^{16} [/tex]

 $2^{16}=2^{16}$

Answer 2

(\frac{1}4} )^{5-x} = 2^{x+3} -logaritmezi in baza e; -exponentul iese in fata; (5-x)*ln(1/4)=(x+3)*ln(2) *ln(a/b)=ln a - ln b; (5-x)ln(1)-(5-x)ln2^{2} =(x+3)*ln(2) ln(1)=0; -2(5-x)ln(2)=(x+3)ln(2) -impartim cu ln 2 -10+2x=x+3 x=13 verificare: (\frac{1}{4} )^{-8} =2^{16} ({2^{-2}})^{-8}=2^{16} 2^{16}=2^{16}