Logaritmai su pagrindais a ir 3

Apskaičiuokite  [tex]\large a^{\left ( \log _32 \right )^{2}}[/tex] reikšmę[tex],[/tex]  kai  [tex]\log _a\frac{1}{9}= \log _32.[/tex]    [tex]a> 0,a≠1.[/tex]

, , m

[tex]\large a^{\left ( \log _32 \right )^{2}}= a^{\log _32\cdot \log _32}= \left ( a^{\log _a\frac{1}{9}} \right )^{\log _32}= \left ( \frac{1}{9} \right )^{\log _32}[/tex][tex]\large = \left ( 3^{-2} \right )^{\log _32}= 3^{-2\log _32}[/tex][tex]\large =[/tex]
[tex]\large =[/tex] [tex]\large 3^{\log _32^{-2}}[/tex][tex]\large =[/tex][tex]\large 2^{-2}= \frac{1}{4}.[/tex]