Question

Tìm x thuộc N , biết:

a)  2^x + 2^x+3  =144

b) (4x -1)² =25 x 9

 

Answer 1

\(a.2^x+2^{x+3}=144\)

\(2^x+2^x.2^3=144\)

\(2^x+2^x.8=144\)

\(2^x.\left(1+8\right)=144\)

\(2^x.9=144\)

\(2^x=144:9\)

\(2^x=16\)

\(2^x=2^4\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

\(b.\left(4.x-1\right)^2=25.9\)

\(\left(4.x-1\right)^2=225^2\)

\(4.x-1=225\)

\(4.x=225+1\)

\(4.x=226\)

\(x=226:4\)

\(x=\frac{226}{4}=\frac{113}{2}\)

Vậy \(x=\frac{113}{2}\)

Answer 2

2^x + 2^x+3 = 144

<=> 2^x + 2^x.2³ = 144

<=> 2^x( 1 + 2³ ) = 144

<=> 2^x.9 = 144

<=> 2^x = 16

<=> 2^x = 2⁴

<=> x = 4

( 4x - 1 )² = 25 . 9

<=> ( 4x - 1 )² = 5² . 3²

<=> ( 4x - 1 )² = ( 5 . 3 )²

<=> ( 4x - 1 )² = 15² = (-15)²

<=> \(\hept{\begin{cases}4x-1=15\\4x-1=-15\end{cases}}\Leftrightarrow\hept{\begin{cases}x=4\\x=-\frac{7}{2}\end{cases}}\)

Answer 3

a) \(2^x+2^{x+3}=144\Leftrightarrow2^x+2^3.2^x=144\Leftrightarrow9.2^x=144\Leftrightarrow2^x=16\Leftrightarrow x=4\)

b) \(\left(4x-1\right)^2=25.9=5^2.3^2=15^2\Leftrightarrow\orbr{\begin{cases}4x-1=15\\4x-1=-15\end{cases}\Leftrightarrow\orbr{\begin{cases}x=4\\x=-3,5\end{cases}}}\)

Nhận \(x=4\)vì \(x\inℕ\)

Answer 4

Bài làm :

\(a,2^x+2^{x+3}=144\)

\(2^x+2^x.2^3=144\)

\(2^x.\left(1+8\right)=144\)

\(2^x.9=144\)

\(2^x=16\)

\(2^x=2^4\)

\(\Rightarrow x=4\)

\(b,\left(4x-1\right)^2=25.9\)

\(\left(4x-1\right)^2=225\)

\(\left(4x-1\right)^2=15^2\)

\(\Rightarrow\orbr{\begin{cases}4x-1=15\\4x=-1=-15\end{cases}}\Rightarrow\orbr{\begin{cases}4x=16\\4x=-14\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=\frac{-7}{2}\end{cases}}\)

Vậy x = 4 hoặc \(x=\frac{-7}{2}\) .

Học tốt

Answer 5

a)  2^x + 2^x+3  =144

\(2^x+2^x.2^3=144\Rightarrow2^x\left(1+8\right)=144\)\(\Rightarrow2^x.9=144\Rightarrow2^x=144:9\Rightarrow2^x=16\)\(\Rightarrow2^x=\orbr{\begin{cases}2^4\\\left(-2\right)^4\end{cases}}\Leftrightarrow=\orbr{\begin{cases}x=4\\x=4\end{cases}}\)

vậy, x=4

b) (4x -1)² =25 x 9

\(\left(4x-1\right)^2=5^2.3^2\)\(\Rightarrow\text{​​}\text{​​}\)\(\left(4x-1\right)^2=15^2\)\(\Leftrightarrow\orbr{\begin{cases}4x-1=15\\4x-1=\left(-15\right)\end{cases}}\Leftrightarrow\orbr{\begin{cases}4x=16\\4x=\left(-14\right)\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=4\\x=\frac{-3}{2}\end{cases}}\)(loại)

vậy, x=4