Question

Вычислить:
log3(0.04)*log5(49)*log7(27)

Answer 1

log₃0,04·log₅49·log₇27 = log₇27·log₃0,04/log₄₉5 = 2log₇27/log₇5 · log₃0,04 =
= 2log₅27·log₃0,04 = 2log₃0,04/log₂₇5 = 6log₃0,04/log₃5 = 6log₅0,04 = 
= 6log₅5⁻² = -12log₅5 = -12

Ответ: -12.

Нужно использовать свойства:
$dfrac{log_cb}{log_ca} = log_ab \ \ log_ab = dfrac{1}{log_ba} \ \ log_{{a}^c}b = dfrac{1}{c} log_ab \ \ log_ab^c = c cdot log_ab \ \ log_aa = 1$