Question

Tìm x biết :

a)3^x+1.15=135

b)x+2.x+2².x+2³.x+...+2²⁰¹⁶.x=2²⁰¹⁷-1

c)x.(x-1)+(x-1)²=0

d)4.32\(\le\)2^x-5\(\le\)1024(x ϵ N)

Answer 1

a) \(3^{x+1}.15=135\)

\(\Rightarrow3^{x+1}=9\)

\(\Rightarrow3^{x+1}=3^2\)

\(\Rightarrow x+1=2\)

\(\Rightarrow x=1\)

Vậy \(x=1\)

Answer 2

b) \(x+2x+2^2x+....+2^{2016}x=2^{2017}-1\\ \Rightarrow x\left(2+2^2+...+2^{2016}\right)=2^{2017}-1\\ \Rightarrow x\left(2^{2017}-2\right)=2^{2017}-1\)

c) \(x\left(x-1\right)+\left(x-1\right)^2=0\\ \Rightarrow x\left(x-1\right)+\left(x-1\right)\left(x-1\right)=0\\ \Rightarrow\left(x-1\right)\left(x+\left(x-1\right)\right)=0\\ \Rightarrow\left(x-1\right)\left(2x-1\right)=0\\ \Rightarrow\begin{cases}x-1=0\\2x-1=0\end{cases}\)

d) \(2^2.2^5\le2^{x-5}\le2^{10}\\ \Rightarrow2^7\le2^{x-5}\le2^{10}\)