16(3) * √2(20)...

EHoTuK @EHoTuK

July 2022 2 5 Report

Найдите натуральное число n, если: (то что в скобках показатель) /-дробь
2(5) * 2(n-1)= 8*4(3)/16(3) * √2(20)

Матов

Verified answer

$2^5*2^{n-1}=\frac{8*4^3}{16^3}*\sqrt{2}^{20}\\
2^{n+4}=\frac{2^9}{2^{12}}*2^{10}\\
2^{n+4}=2^7\\
n+4=7\\
n=3$

1 votes Thanks 1

mmb1

Verified answer

2(5) * 2(n-1)= 8*4(3)/16(3) * √2(20)
$2^5*2^{n-1}=8^3/16^3* \sqrt{2^{20}}
$
$2^52^{n-1}=(2^3)^3/(2^4)^3*2^{10}
$
$2^{n+4}=2^92^{10}2^{-12}$
$2^{n+4}=2^{7}
n+4=7
n=3$

1 votes Thanks 1

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