1) 5log b^2/a (a^2/b); если log a (b)=3
log a (a^2/b) log a (a^2) - log a (b)
5log (b^2)/a (a^2/b)= 5· ------------------ = 5· --------------------------- =
log a (b^2)/a log a (b^2)-log a (a)
2- 3 (-1)
= 5 --------- = 5 ---- = -1
2·3 -1 5
2) log 2 (a^1/3) , если log 4 (a^3)=9
log 4 (a^3)=9 ⇔3 log 4 (a)=9 ⇔ log 4 (a)=3
log 4 (a^1/3) (1/3)log 4 (a) 1log 2 (a^1/3) = ---------------- = ----------------- = ------ = 2
log 4 (2) log 4 (√4) 1/2
3) lg2.5 если log 4(125) = a
log 4(125) = a ⇔ log 4(5³) =3 log 4(5) =a ⇔ log 4(5)=a/3
log 4 (5/2) log 4 (5)-log 4 (2) a/3-1/2 2a-3lg2.5 =-------------- = ------------------------- = ----------- = ---------
log 4 (5·2) log 4 (5) +log 4 (2) a/3 +1/2 2a+3