Question

a ] [x ^54] ^2 = x

b] [ 2 ^x+3 + 2^x = 144

ai nhanh mk cho tk nha

gai ro ra nha

thanks

Answer 1

\(a.\left(x^{54}\right)^2=x\)

\(\Rightarrow x^{108}=x\)

\(\Leftrightarrow x^{108}-x=0\)

\(\Leftrightarrow x.\left(x^{107}-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^{107}=0\Leftrightarrow x^{107}=1\Leftrightarrow x=1\end{cases}}\)

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

Answer 2

a) ( x⁵⁴ )² = x

=> ( x⁵⁴ )² - x = 0

=> x¹⁰⁸ - x = 0

=> x(x¹⁰⁷ - 1 ) = 0

=> x¹⁰⁷ - 1 = 0

=> x¹⁰⁷ = 1

=> x¹⁰⁷ = 1¹⁰⁷

=> x = 1

b)  2^x+3+ 2^x = 144

=> 2^x . 2³ + 2^x = 144

=> 2^x . ( 2³ + 1 ) = 144

=> 2^x . 9 = 144

=> 2^x = 16

=>  x = 4

Answer 3

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

\(\Leftrightarrow2^x.2^3+2^x=144\)

\(\Leftrightarrow2^x.\left(8+1\right)=144\)

\(\Leftrightarrow2^x.9=144\)

\(\Leftrightarrow2^x=144:9=16\)

\(\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)