Cho a = log3(15), b = log3(10). Hãy tính log căn3(50) theo a và b.

* Hướng dẫn giải

Ta có:

a = ${\log }_{3}15$ = ${\log }_3\left(3.5\right)$ = ${\log }_{3}3$ + ${\log }_{3}5$ = 1 + ${\log }_{3}5$

Suy ra ${\log }_{3}5$ = a – 1

b = ${\log }_{3}10$ = ${\log }_3\left(2.5\right)$ = ${\log }_{3}2$ + ${\log }_{3}5$

Suy ra ${\log }_{3}2$ = b − ${\log }_{3}5$ = b − (a − 1) = b – a + 1

Do đó:

${\log }_{\sqrt{3}}50$ = ${{\log }_3}^{0,5}\left(2.52\right)$ = 2${\log }_{3}2$ + 4${\log }_{3}5$ = 2 (b – a + 1) + 4(a − 1) = 2a + 2b − 2