Răspuns:
Explicație pas cu pas:
a) 3^x²=3^4 ⇒x²=4 ⇒ x=±2
b)notam a=3^x si b=4^x ⇒5a²-7ab+2b²=0 5a²-5ab-2ab+2b²=0
5a(a-b)-2b(a-b)=0 ⇒(a-b)(5a-2b(=0
1)a-b=0 ⇒3^x=4^x (3/4)^x=1⇒ sol 1 x=0
2) 5a=2b (3/4)^x=2/5
logaritmam in baza 10 ⇒xlg(3/4)=lg(4/10) x=lg(2/5)/lg(3/4)
c) 3^(x-2)×(3²+3³+1)=37 ⇒3^(x-2)=1 ⇒x-2=0 x=2
d) notam t=3^x
t²-12t+27=0 t1,2=6±√36-27=6±3
t1=9 ⇒3^x=9 ⇒x=2
t2=3 ⇒3^x=3 ⇒x=1
