Question

[pham nhu nguyen]

7^5x : 49 =7 ²⁸

2^x - 5 =27

(x⁴)⁵ = x

Answer 1

[Xyz OLM]

7^5x : 49 = 7²⁸

=> 7^5x : 7² = 7²⁸

=> 7^{5x - 2}    = 28

=>   5x - 2  = 28

=>   5x        = 30

=>     x        = 30 : 5

=>     x        = 6

b) 2^x - 5 = 27

=> 2^x     = 27 + 5

=> 2^x     = 32

=> 2^x     = 2⁵

=>   x     = 5

c) (x⁴)⁵ = x

=> x^4.5 = x

=> x²⁰  = x

=> x²⁰ - x = 0

=> x(x¹⁹ - 1) = 0

=> \(\orbr{\begin{cases}x=0\\x^{19}-1=0\end{cases}}\)=> \(\orbr{\begin{cases}x=0\\x^{19}=1\end{cases}}\)=> \(\orbr{\begin{cases}x=0\\x^{19}=1^{19}\end{cases}}\)=> \(\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)

Vậy \(x\in\left\{-1;0;1\right\}\)

Answer 2

[๖ۣۜҨž ♫ ℱ¡ɗℰ£¡ɑ๖²⁴ʱ]

\(a,7^{5x}:49=7^{28}\)

\(7^{5x}:7^2=7^{28}\)

\(7^{5x-2}=7^{28}\)

\(\Rightarrow5x-2=28\)\(\Rightarrow5x=30\)\(\Rightarrow x=6\)

\(b,2^x-5=27\)\(\Rightarrow2^x=32\)\(\Rightarrow2^x=2^5\Rightarrow x=5\)

\(c,\left(x^4\right)^5=x\)

\(\Rightarrow x^{20}=x\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)