a) Cho a =

- Hướng dẫn giải

a) Ta có:

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

Suy ra ${\log }_{3}5$ = a – 1

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

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

Do đó:

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

b) Ta có:

${\log }_{140}63$ = ${\log }_{140}(32.7)$ = 2${\log }_{140}3$ + ${\log }_{140}7$

Từ đề bài suy ra:

${\log }_{0,5}\mathrm{\pi }.{\log }_{7}5$ = ${\log }_{7}2.{\log }_{2}3.{\log }_{35}$ = cab

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