Question

Giúp mình câu 23;24;25;26

Answer 1

26: \(\left(\frac23\right)^{x+2}+\left(\frac23\right)^{x+1}=\frac{20}{27}\)

=>\(\left(\frac23\right)^{x}\cdot\left\lbrack\left(\frac23\right)^2+\frac23\right\rbrack=\frac{20}{27}\)

=>\(\left(\frac23\right)^{x}\cdot\left(\frac49+\frac23\right)=\frac{20}{27}\)

=>\(\left(\frac23\right)^{x}\cdot\frac{10}{9}=\frac{20}{27}\)

=>\(\left(\frac23\right)^{x}=\frac23\)

=>x=1

25: \(\left(\frac15\right)^{x+1}-\left(\frac15\right)^{x}=\frac{-4}{625}\)

=>\(\left(\frac15\right)^{x}\left(\frac15-1\right)=\frac{-4}{625}\)

=>\(\left(\frac15\right)^{x}\cdot\frac{-4}{5}=\frac{-4}{625}\)

=>\(\left(\frac15\right)^{x}=\frac{1}{125}=\left(\frac15\right)^3\)

=>x=3

24: \(3^{x+5}+3^{x+2}=756\)

=>\(3^{x}\cdot243+3^{x}\cdot9=756\)

=>\(3^{x}\cdot252=756\)

=>\(3^{x}=\frac{756}{252}=3=3^1\)

=>x=1

23: \(2^{x+2}-2^{x+1}=32\)

=>\(2^{x}\cdot4-2^{x}\cdot2=32\)

=>\(2^{x}\cdot2=32\)

=>\(2^{x}=16=2^4\)

=>x=4