Question

Tìm số tự nhiên n, biết :
a ) 2ⁿ = 8 ;         b ) 5^{2n - 3} = 125 ;

c ) 8ⁿ : 4 = 128 ;          d ) 7^{n - 2} . 7⁴ = 7⁴

Answer 1

`a. 2^n = 2^3`

`=> n=3`

`b, 5^(2n-3) = 125`

`=> 2n-3=3`

`=> n = 3`.

`c,4^(2n) : 4 = 4^(2n-1) = 7`

`=> 2n-1=7->n=4`

`d, 7^(n-2+4) = 7^4`

`=> n-2+4=4`

`=> n=2`

Answer 2

`a)2^n=8`

`2^n=2^3`

`n=3`

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`b)5^[2n-3]=125`

`5^[2n]:5^3=125`

`5^[2n]=5^3 .5^3=5^6`

`2n=6`

`n=3`

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`c)8^n:4=128`

`8^n=128.4=512`

`8^n=8^3`

`n=3`

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`d)7^[n-2],7^4=7^4`

`7^[n-2]=7^4:7^4=1`

`7^[n-2]=7^0`

`n-2=0`

`n=2`

Answer 3

\(a.2^n=8\)

\(\Leftrightarrow2^n=2^3\)

\(\Leftrightarrow n=3\)

\(b.5^{2n-3}=125\)

\(\Leftrightarrow5^{2n-3}=5^3\)

\(\Leftrightarrow2n-3=3\)

\(\Leftrightarrow n=3\)

\(c.8^n:4=128\)

\(\Leftrightarrow2^{3n}:2^2=128\)

\(\Leftrightarrow2^{3n-2}=2^7\)

\(\Leftrightarrow3n-2=7\)

\(\Leftrightarrow n=3\)

\(d.7^{n-2}.7^4=7^4\)

\(\Leftrightarrow7^{n-2}=1\)

\(\Leftrightarrow n-2=0\)

\(\Leftrightarrow n=2\)