Задача 75559 a) (-2)^8 · 5^3 ________ 5^4 ·...

65b2ac633f7efb2eafdda015

1/25/2024 6:47:00 PM

a) (-2)^8 · 5^3
________
5^4 · 2^10 · 10

b) log_2 16 + log_(1/2) 4 - log_(sqrt(15)) 15

626fab9a354ab65fb2f43abb

1/25/2024 8:00:18 PM

★

a) [m]\frac{(-2)^8 \cdot 5^3}{5^4 \cdot 2^{10} \cdot 10} = \frac{2^8 \cdot 5^3}{5^4 \cdot 2^{10} \cdot 2 \cdot 5} =[/m]
[m]= \frac{2^8 \cdot 5^3}{5^5 \cdot 2^{11}} = \frac{1}{5^2 \cdot 2^3} = \frac{1}{25 \cdot 8} = \frac{1}{200} = 0,005[/m]

b) [m]log_2(16) + log_{1/2}(4) - log_{\sqrt{15}}(15) = 4 - 2 - 2 = 0[/m]