Question

Вычислите log12 1/144-(2/3)^1/2 (27/8)^1/3

Answer 1

$log_{12}frac{1}{144}-left(frac{2}{3}right)^frac{1}{2}cdotleft(frac{27}{8}right)^frac{1}{3}=log_{12}144^{-1}-left(frac{2}{3}right)^frac{1}{2}cdotleft(frac{3^3}{2^3}right)^frac{1}{3}\\=-log_{12}12^2-left(frac{2}{3}right)^frac{1}{2}cdotfrac{3}{2}=-2log_{12}12-left(frac{2}{3}right)^frac{1}{2}cdotleft(frac{2}{3}right)^{-1}=-2-left(frac{2}{3}right)^{frac{1}{2}-1}$

$=-2-left(frac{2}{3}right)^{-frac{1}{2}}=-2-left(frac{3}{2}right)^frac{1}{2}=-2-sqrtfrac{3}{2}=-2-frac{sqrt3}{sqrt2}cdotfrac{sqrt2}{sqrt2}=-2-frac{sqrt6}{2}\\=-frac{4}{2}-frac{sqrt6}{2}=-frac{4+sqrt6}{2}$


$-2-frac{sqrt6}{2}=-2-0,5sqrt6approx-2-0,5cdot2,45=-3,225$

Answer 2

А в десятичной дроби?