Ответ:

Объяснение:

1)Значение а, если log3 (a) = 1/2; a = 3^(1/2) = √3

2)Значение b,если log(b) (1/81) = -4; b^(-4) = 1/81 = 3^(-4); b = 3

3)Значение c,если log6 (c) = 3; c = 6^3 = 216

4)Значение m,если log(m) (0.25) = -4; m^(-4) = 0,25 = (√2)^(-4); m = √2

2.Если log(7) 3 = a и log(7) 5 = b,то найдите:

1)log(7) 25 - log(7) 243 = log(7) (5^2) - log(7) (3^5) = 2log(7) 5 - 5log(7) 3 =

= 2b - 5a

2)log(125) 81 + 2log(7) 15 = log(5^3) (3^4) + 2(log(7) 3 + log(7) 5) = A

Заметим, что log(5) 3 = log(7) 3 : log(7) 5 = a/b. Отсюда

log(5^3) (3^4) = (4log(7) 3) : (3log(7) 5) = 4a/(3b)

Возвращаемся к примеру:

A = log(5^3) (3^4) + 2(log(7) 3 + log(7) 5) = 4a/(3b) + 2(a + b)

3)1/2log(7) 441 - log(5) 9 = log(7) (√441) - 2log(5) 3 = log(7) 21 - 2a/b =

= log(7) 3 + log(7) 7 - 2a/b = a + 1 - 2a/b

4)log(15) 21+3log(15) 245 = log(7) 21 / (log(7) 15) + 3log(7) 245 / (log(7) 15) =

= [log(7) 3 + log(7) 7 + 3log(7) (5*7^2)] / (log(7) 15) =

= [a + 1 + 3(log(7) 5 + log(7) 7^2)] / (log(7) 3 + log(7) 5) =

= [a + 1 + 3(b + 2)] / (a + b) = (a + 3b + 7) / (a + b)