Question

со степенями и логарифмами

Answer 1

$27^{\frac{2}{3}}=(3^3)^{\frac{2}{3}}=3^{3*\frac{2}{3}}=3^2=9$

$3^{\frac{2}{7}}*3^{\frac{5}{7} }=3^{\frac{2}{7}+\frac{5}{7}}=3^1=3$

$log_3\frac{1}{9} =log_3(\frac{1}{3})^2 =log_33^{-2}=-2*log_33=-2*1=-2$

$log_215-log_2\frac{15}{16} =log_2(\frac{15}{\frac{15}{16}} )=log_2(16*\frac{15}{15})=log_2(16*1)=log_216=log_2(2^4)=4log_22=4*1=4$

Answer 2

а)$27^{\frac{2}{3} } = \sqrt[3]{27^{2} } =\sqrt[3]{3^{6} } = {3^{2} } = 9$

$27^{\frac{2}{3} } = 3^{3*\frac{2}{3} } = 3^{2} = 9$

б) $3^{\frac{2}{7} } * 3^{\frac{5}{7} } = 3^{\frac{2}{7}+\frac{5}{7} } =3^{1} = 3$

в) $log_{3}\frac{1}{9} = -2$

г)$log_{2}15 - log_{2}\frac{15}{16} = log_{2}(15:\frac{15}{16}) = log_{2}16 = 4$