Question

e)2^-2.2^x+2.2^x=9.2⁶ f)3^-22.3⁴.3^x=3⁷

Answer 1

e; 2\(^{-2}\).2\(^{x}\) + 2.2\(^{x}\) = 9.2\(^6\)

2\(^{x}\).(\(\frac14\) + 2) = 9.64

2\(^{x}\).(\(\frac14+\frac84\)) = \(576\)

2\(^{x}\).\(\frac94\) = 576

2\(^{x}\) = 576 : \(\frac94\)

2\(^{x}\) = 256

2\(^{x}\) = 2\(^8\)

\(x=8\)

Vậy \(x=8\)

Answer 2

e: \(2^{-2}\cdot2^{x}+2\cdot2^{x}=9\cdot2^6\)

=>\(2^{x}\left(2+2^{-2}\right)=9\cdot2^6\)

=>\(2^{x}\left(2+\frac14\right)=9\cdot2^6\)

=>\(2^{x}\cdot\frac94=\frac94\cdot2^8\)

=>\(2^{x}=2^8\)

=>x=8

f: \(3^{-22}\cdot3^4\cdot3^{x}=3^7\)

=>\(3^{x+4-22}=3^7\)

=>x-18=7

=>x=18+7=25

Answer 3

x=8