помогите
найти
[tex] log_{ {a}^{2} b}(ab) [/tex]
если
[tex] log_{ \frac{b}{a} }( \frac{ {a}^{2} }{b} ) = - \frac{1}{2} [/tex]
найти
[tex] log_{ {a}^{2} b}(ab) [/tex]
если
[tex] log_{ \frac{b}{a} }( \frac{ {a}^{2} }{b} ) = - \frac{1}{2} [/tex]
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Объяснение:
Найти
, если 
Ответ:
Verified answer
Ответ: 4/5
Объяснение:
Первый способ.
log(b/a; a^2/b) = log(b/a; a/b) + log(b/a; a) = -1/2
-1 + log(b/a; a) =-1/2
log(b/a; a) = 1/2
log(a; b/a) = 2
log(a; 1/a) +log(a;b) = 2
-1 + log(a; b) = 2
log(a; b) = 3
log(ab; a^2*b) = log(ab; ab) +log(ab; a) =
=1+ 1/log(a; ab) = 1+1/( log(a;a) +log(a;b) = 1+ 1/4 = 5/4
log(a^2*b; ab) = 1/(5/4) = 4/5
Второй способ.
log(b/a; a^2/b) = -1/2
(b/a)^(-1/2) = a^2/b
a/b =a^4/b^2
a^3=b
log(a^2*b; ab) = log(a^5; a^4) = 4/5