Question

Daca log in baza 3 din x=5 si log in baza 3 din y= 2 , sa se afle log in baza y din x

Answer 1

㏒3din x=5 => x=$3^{5}$
log3y=2 => y=3^2

logydin x = log$3^{2}$din 3^5 = 5/2

Answer 2

$\displaystyle log_3x=5 \\ \\ 5=log_33^5=log_3243 \\ \\ log_3x=5 \Rightarrow log_3x=log_3243 \Rightarrow x=243 \\ \\ log_3y=2 \\ \\ 2=log_33^2=log_39 \\ \\ log_3y=2 \Rightarrow log_3y=log_39 \Rightarrow y=9 \\ \\ log_yx=log_9243=log_99^ \frac{5}{2} = \frac{5}{2} log_99= \frac{5}{2} \\ \\ \boxed{log_yx= \frac{5}{2} }$