Question

ma ajuta si pe mine cinea la ecuatii exponentiale?
12^2x+2=15
2\5^x-1 * 25|8^x-1=125=64

Answer 1

1) $12^{x+1}=15,logaritmam,in,baza,12: log_{12} 12^{x+1}= log_{12}15$, exponentul trece in fata si log in baza12 din 12 =1: 
[tex](x+1) log_{12}12= log_{12}15,deci,x+1= log_{12}15,de,unde x= log_{12}15-1 [/tex]=$log_{12}15- log_{12}12= log_{12} \frac{15}{12} }.$
2) $(\frac{2}{5}) ^{x-1}* (\frac{25}{8}) ^{x-1}= \frac{125}{64}$ ⇒
$(\frac{2*25}{5*8}) ^{x-1}= \frac{125}{64},deci, (\frac{5}{4} )^{x-1}= (\frac{5}{4}) ^{3},adica,x-1=3,sau x=4.$