1.
a. 9 < \(^{3^y}\)< 81
9=3\(^{^2}\)
81=3\(^{^4}\)
\(\Rightarrow\)y=3 vì \(3^2< 3^3< 3^4\)
b.25\(\le\)5\(^{^y}\)\(\le\)125
25=5\(^{^2}\)
125=5\(^{^3}\)
\(\Rightarrow\)y=2 và 3 vì 5\(^{^2}\)\(\le\)5\(^{^2}\)(5\(^{^3}\))\(\le\)5\(^{^3}\)
c.
16\(\ge\)4\(^{^y}\)\(\ge\)1024
16=4\(^{^2}\)
1024=4\(^{^5}\)
\(\Rightarrow\)y=2,3,4,5 vì 4\(^{^2}\)\(\ge\)4\(^{^2\left(4^3;4^4;4^5\right)}\)
\(^{^2}\)
\(\Rightarrow\)
2.
a.3x\(^{2^y}\)=48
\(^{2^y}\)=48:3
\(^{2^y}\)=16
\(\Rightarrow\)y=4 vì \(^{2^4}\)=16
b.5x\(y^7\)=640
\(y^7\)=640:5
\(y^7\)=128
\(\Rightarrow\)y=2 vì \(2^7\)=128
c.\(y^{100}\)=\(y^2\)
\(\Rightarrow\)y=1 vì:
\(1^{100}\)=1
\(1^2\)=1
d.(y-3)\(^{^5}\)=243
\(\Rightarrow\)y-3=3 vì 3\(^{^5}\)=243
y=3+3
y=6
e.(2y+1)\(^{^3}\)=125
\(\Rightarrow\)2y+1=5 vì 5\(^{^3}\)=125
2y=5-1=4
y=4:2=2
i.2\(^{^{y+3}}\)+2\(^{^y}\)=288
2\(^{^y}\).2\(^{^3}\)+2\(^{^y}\)=288
2\(^{^y}\).2\(^{^3}\)=288-2\(^{^y}\)
2\(^{^y}\).8=288-2\(^{^y}\)
8=(288-2\(^{^y}\)):2\(^{^y}\)
8=288:2\(^{^y}\)-2\(^{^y}\):2\(^{^y}\)
8=288:2\(^{^y}\)-1
288:2\(^{^y}\)=8+1=9
2\(^{^y}\)=288:9=32
\(\Rightarrow\)y=5 vì 2\(^{^5}\)=32