Question

Sa se rezolve urmatoarele ecuatii logaritmice:
a) 7 la puterea x-2=4
B)4 la puterea radical din x+1=8

Answer 1

Sunt ecuatii exponentiale, care au ca radacini logaritmi.
a) $7^{x-2} =4,logaritmam,in,baza,7,deci, log_{7} 7^{x-2}=log_{7}4$ exponentul coboara in fata iar $log_{7}7=1$,deci,obtinem,x-2= $log_{7}4$[/tex],sau,x=2+log_{7}4= log_{7}7^2 [/tex]}=$log_{7}4$+$log_{7}49$= log_{7} $\frac{4}{49}$
b) $4^{x+1}=8,sau, 2^{2(x+1)}= 2^{3}$, de unde 2(x+1)=3 ⇒2x+2=3
deci x=$\frac{1}{2}$