Question

a) 2^x . 4 = 128

b) (2x + 1 ) 3 = 125

c) 2^x - 26 = 6

d) 64 . 4^x = 4⁵

e) 27 . 3^x = 243

g) 49 . 7^x = 2041

Answer 1

a) \(\Rightarrow2^x=32\Rightarrow2^x=2^5\Rightarrow x=5\)

b) \(\Rightarrow\left(2x+1\right)^3=5^3\)

\(\Rightarrow2x+1=5\Rightarrow x=2\)

c) \(\Rightarrow2^x=32\Rightarrow x=5\)

d) \(\Rightarrow4^3.4^x=4^5\Rightarrow4^x=4^2\Rightarrow x=2\)

e) \(\Rightarrow3^3.3^x=3^5\Rightarrow3^x=3^2\Rightarrow x=2\)

f) \(\Rightarrow7^2.7^x=7^4\Rightarrow7^x=7^2\Rightarrow x=2\)

Answer 2

a. 2^x . 4 = 128

<=> 2^{x + 2} = 2⁷

<=> x + 2 = 7

<=> x = 5

b. (2x + 1)³ = 125

<=> (2x + 1)³ - 5³ = 0

<=> (2x + 1 - 5)\(\left[\left(2x+1\right)^2+\left(2x+1\right).5+25\right]=0\)

<=> (2x - 4)(4x² + 4x + 1 + 10x + 5 + 25) = 0

<=> (2x - 4)(4x² + 14x + 31) = 0

<=> \(\left[{}\begin{matrix}2x-4=0\\4x^2+14x+31=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=2\\VôNghiệm\end{matrix}\right.\)

c. 2^x - 26 = 6

<=> 2^x = 32

<=> x = 5

d. 64 . 4^x = 4⁵

<=> 4³ . 4^x = 4⁵

<=> 4^{3 + x} = 4⁵

<=> 3 + x = 5

<=> x = 2

e. 27 . 3^x = 243

<=> 3³ . 3^x = 3⁵

<=> 3^{3 + x} = 3⁵

<=> 3 + x = 5

<=> x = 2

g. 49 . 7^x = 2401 (Bn xem lại đề câu này)

<=> 7² . 7^x = 7⁴

<=> 7^{2 + x} = 7⁴

<=> 2 + x = 4

<=> x = 2

Answer 3

a, 2^x.4= 128

=> 2^x= 128:4

=>2^x= 32

=> 2^x=2⁵

=> x=5

\(\left(2x+1\right)^3=125\)

\(\Rightarrow\left(2x+1\right)^3=\left(\pm5\right)^3\)

\(\Rightarrow\left[{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=4\\2x=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

c, 2^x - 26 = 6

=> 2^x = 32

=> 2^x= 2⁵

=> x=5 

d, 64. 4^x = 4⁵

=> 4³. 4^x= 4⁵

=> 3+x=5

=> x=2

e, 27. 3^x= 243

=> 3³. 3^x= 3⁵

=> 3+x=5

=> x=2

Hoctot