Question

Sa se determine baza logaritmilor
Log in baza a din din 2 = 4
Log in baza a din 3=1/3
Log in baza a din radical din 3=1/2
Log in baza a din 1/25=-2

Answer 1

$log_{a}3= \frac{1}{3},deci,a^ \frac{1}{3}=3,sau,a=3^3=27$$log_{a}2=4,adica,a^4=2,deci,a= \sqrt[4]{2}$
$log_{a} \sqrt{3}= \frac{1}{2},echivalent,cu,a^ \frac{1}{2}= \sqrt{3} ,sau,a=3$
$log_{a} \frac{1}{25}=-2,deci,a^{-2} = \frac{1}{25},sau,(a^{-2})^{-1}=( \frac{1}{25}) ^{-1}} },sau,a^2=25,deci$,a=5.

Answer 2

a) $a^{4} =2 , a= \sqrt[4]{2}$

b) $a^{1/3} =3$, 
    $\sqrt[3]{a}=3$, 
a=3³=27
c) a^{1/2}=√3
    √a=√3 ⇒ a=3

d) a^{-2}=1/25 ⇒1/a²=1/25
a²=25 ⇒ a=5