Verified answer

а) Замена основания: log32(125) = lg125/lg32 =

=2,096910013/1,505149978 = 1,393156857.

Можно использовать свойство логарифмов: 125 = 5³, 32 = 2^5.

loga^q(b^p) = (p/q)loga(b) = (3/5)*(lg5/lg2) = 0,6*(0,698970004/ 0,301029996) = 0,6*2,321928095 =1,393156857.

б) log81(256) = lg256/lg81 = 2,408239965/1,908485019 = 1,261859507.

256 = 2^8, 81 = 3^4.

(8/4)*lg2/lg3) = 2*(0,301029996/0,477121255) = 2*0,630929754 =

= 1,261859507.