Question

Задание 1.
log 25 35, если log5 7 = a.

Задание 2.
Решить:
Log3(log2 5×log5 8)

Answer 1

Задание 1.
log₂₅35 = (1/2) • log₅ • (5 • 7) = (1/2) • (log₅5 + log₅7) = (1/2) • (1 +log₅7) = (1/2) • (1 + a).

Задание 2.
log₃ • (log₂5 • log₅8) = log₃ • (log₂5 • log₅2³) = log₃ • (log₂5 • 3 • log₅2) = log₃(3 • log₂5/log₂5) = log₃3 = 1.

Answer 2

$log_{25} 35 =log_{5^2} (5*7)= \frac{1}{2} log_5 (5*7)= \frac{1}{2} (log_5 5+log_5 7)=\\= \frac{1}{2} (1+a)=$

$log_3 (log_2 5*log_5 8)=log_3 ( \frac{log_5 8}{log_5 2} )=log_3 (log_2 8)=log_3 3=1$