Đáp án`+`Giải thích các bước giải:
` d) 2^(-1) .2^n + 4 .2^n = 9 . 2^5 `
`-> 2^n .(2^(-1) +4) = 9 + 2^5`
`-> 2^n . 9/2 = 9. 2^5`
`-> 2^n = 9 . 2^5 . 9/2 `
`-> 2^n = 2^5 . 2 = 2^6 `
`-> n =6`
`B2:`
` a) 125.5 ` $\geq$ `5^n`$\geq$ `5.25`
`-> 625 `$\geq$ `5^n`$\geq$ `125`
`-> `5^4`$\geq$ `5^n`$\geq$ `5^3`
`-> n ∈{4;3}`
` b)(n^54)^2 = n `
`-> n^108 = n`
`-> n^108 -n=0`
`-> n .(n^107 - 1)=0`
`-> `\(\left[ \begin{array}{l}n=0\\n ^107-1=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=0\\n=1\end{array} \right.\)
`c) 243 `$\geq$ `3^n`$\geq$ `9.27`
`-> 243` $\geq$ `3^n`$\geq$ `243`
`->3^5`$\geq$ `3^n`$\geq$ 3^5`
`-> n = 5`
` d) 2^(n+3) .2^n= 144`
`-> 2^n . 2^3 . 2^n = 144`
`-> 2^(2n) .8 = 144`
`-> 2^(2n) 144:8 = 18 = 2.9 `(vô lý)
Vậy `n∈` tập hợp rỗng
