Question

ДАЮ 50 БАЛОВ!!!!
найдите х, если:

1) log_6(x) = 3 * log_6(2) + 0, 5 * log_6(25) - 2 * log_6(3) ;

2) lgx = 1/3 * lg(5a) - 2lgb + 5lgc

3) lgx = 3lgm + 2/7 * lgn - 1/5 * lgp

4) log_3(x) = 1/3 * log_3(8) - 2 * log_3(20) - 3 * log_3(2)
​

Answer 1

Ответ:

log_6(x) = 3 * log_6(2) + 0,5 * log_6(25) - 2 * log_6(3)

log_6(x) = log_6(2^3) + log_6(25^0,5) - log_6(3^2)

log_6(x) = log_6(8) + log_6(5) - log_6(9)

log_6(x) = log_6(8 * 5) - log_6(9)

log_6(x) = log_6(40 / 9)

x = 40 / 9

lgx = 1/3 * lg(5a) - 2lgb + 5lgc

lgx = lg(5a)^(1/3) - lg(b^2) + lg(c^5)

lgx = lg(5^(1/3) * a^(1/3) * c^5 / b^2)

x = 5^(1/3) * a^(1/3) * c^5 / b^2

lgx = 3lgm + 2/7 * lgn - 1/5 * lgp

lgx = lg(m^3) + lg(n^(2/7)) - lg(p^(1/5))

lgx = lg(m^3 * n^(2/7) / p^(1/5))

x = m^3 * n^(2/7) / p^(1/5)

log_3(x) = 1/3 * log_3(8) - 2 * log_3(20) - 3 * log_3(2)

log_3(x) = log_3(8^(1/3)) - log_3(20^2) - log_3(2^3)

log_3(x) = log_3(2) - log_3(400) - log_3(8)

log_3(x) = log_3(2 / (400 * 8))

log_3(x) = log_3(1/1600)

x = 1/1600

Answer 2

Пошаговое объяснение:

В третьем уравнении х равен тому, что в скобках)