Question

вычислите ..........................

Answer 1

Ответ:

$1)\ \frac{2}{3}$

$2)\ 1\frac{1}{3}$

$3)\ -21$

$4)\ 1$

Объяснение:

$1)\\\\\frac{1}{log_927}=\frac{1}{\frac{lg27}{lg9}}=\frac{lg9}{lg27}=\frac{lg3^2}{lg3^3}=\frac{2lg3}{1lg3}=\frac{2}{3}$

$2)\\\\\frac{1}{log_{16}8}=\frac{1}{\frac{lg8}{lg16}}=\frac{lg16}{lg8}=\frac{lg2^4}{lg2^3}=\frac{4lg2}{3lg2}=\frac{4}{3}=1\frac{1}{3}$

$3)\\\\log_2128\cdot log_5\frac{1}{125}=log_22^7\cdot log_55^{-3}=7log_22\cdot(-3)log_55=7\cdot (-3)=-21$

$4)\\\\log_3(log_25\cdotlog_58) =log_3(\frac{lg5}{lg2}\cdot \frac{lg8}{lg5}) =log_3(\frac{lg8}{lg2}) =\\\\log_3(\frac{lg2^3}{lg2})=log_3(\frac{3lg2}{lg2}) log_33=1$