помогите
найти

если

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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