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\(a;5^{23}=5\cdot5^{22}< 6\cdot5^{22}\Rightarrow5^{23}< 6\cdot5^{22}\)
\(b;7\cdot2^{13}< 8\cdot2^{13}=2^3\cdot2^{13}=2^{15}\)
\(c;21^{15}=3^{15}\cdot7^{15}>3^{15}\cdot7^{14}=27^5\cdot49^8\)
\(d;199^{20}< 200^{20}=10^{40}\cdot2^{20}< 10^{45}\cdot2^{15}=2000^{15}< 2001^{15}\)
\(e;3^{39}=9^{13}< 11^{13}< 11^{21}\)
a) 2^n=128/4=32=2^5\(\Rightarrow\)n=5
b)3^n+1 :9=81\(\Rightarrow\)3^n.3 :9=81\(\Rightarrow\)3^n:3=81\(\Rightarrow\)3^n =243=3^5\(\Rightarrow\)n=5
c) 15^n:15=(3^2)^2:3^4=3^4:3^4=1\(\Rightarrow\)15^n=15=15^1\(\Rightarrow\)n=1
a, <=> 2^n = 128/4 = 32
<=> 2^n = 2^5
<=> n =5
b,<=> 3^(n+1) = 81.9= 729
<=> 3^(n+1) = 3^6
<=> n+1 = 6 <=> n =5
c, <=> 15^(n-1) = 1
<=> 15^(n-1) = 15^ 0
<=> n-1 = 0 <=> n =1
=\((11.3^{29}-\left(3^2\right)^{15}):(2^2.3^{28})\)
=\((11.3^{29}-3^{30}):(2^2.3^{28})\)
=\((11.3^{29}-(3^{29}.3):(2^2.3^{28})\)
=\(\frac{3^{29}.(11-3)}{3^{28}.4}\)
=\(\frac{3.8}{4}\)=\(\frac{3.2}{1}\)=6
Ta có: \(7\cdot2^{13}-2^{15}\)
\(=2^{13}\cdot\left(7-2^2\right)\)
\(=3\cdot2^{13}\)
Ta có: \(2\cdot3^{16}-17\cdot3^{14}\)
\(=3^{14}\cdot\left(2\cdot3^2-17\right)\)
\(=3^{14}\cdot\left(18-17\right)=3^{14}\)
\(=3\cdot3^{13}>3\cdot2^{13}=7\cdot2^{13}-2^{15}\)