( 34 . 24 . 5 )199+323:321.230
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a) \(2^{24}< 3^{16}\)
b) \(3^{34}>5^{20}\)
c) \(\left(3\cdot24\right)^{100}< 3^{300}+4^{300}\)
d) \(199^{20}>200^{15}\)
1: \(=-145\cdot13+145\cdot57+57\cdot10-57\cdot145=-1315\)
2: \(=17\cdot15-17\cdot16+16\cdot17-16\cdot20=255-320=-65\)
3: \(=-38\cdot25+38\cdot4-25\cdot4+25\cdot38=13\cdot4=52\)
4: \(=23\cdot145-23\cdot17-145\cdot23+145\cdot6=479\)
5: \(=24\cdot15-24\cdot4+4\cdot24-4\cdot15=360-60=300\)
6: \(=199\left(15-17+17-5\right)=199\cdot10=1990\)
7: \(=-39\cdot5+39\cdot99+99\cdot10-99\cdot39=795\)
\(2^x:4=32\\ \Rightarrow2^x=128\\ \Rightarrow2^x=2^7\\ \Rightarrow x=7\)
\(3^{x-2}:3=243\\ \Rightarrow3^{x-2}=729\\ \Rightarrow3^{x-2}=3^6\\ \Rightarrow x-2=6\\ \Rightarrow x=8\)
\(256:4^{x+1}=4^2\\ \Rightarrow4^{x+1}=4^2\\ \Rightarrow x+1=2\\ \Rightarrow x=1\)
\(4^{2x-1}:4=4^4\\ \Rightarrow4^{2x-1}=4^5\\ \Rightarrow2x-1=5\\ \Rightarrow x=3\)
\(5^{x-1}:5=5^3\\ \Rightarrow5^{x-1}=5^4\\ \Rightarrow x-1=4\\ \Rightarrow x=5\)
\(3^{2x+1}:3=3^4\\ \Rightarrow3^{2x+1}=3^5\\ \Rightarrow2x+1=5\\ \Rightarrow x=3\)
\(\frac{323}{34}+\frac{34}{345}\times84=17\frac{179}{230}\)
5. ( - 199 ) + ( - 200 ) + ( - 201 )
= [ ( - 199 ) + ( - 20 ) ] + ( - 200 )
= ( - 400 ) + ( - 200 )
= - 600
\(-9-13-\left(-24\right)+11\)
\(=\left(-9-13\right)+\left(24+11\right)\)
\(=-22+35\)
\(=13\)
Bài 1:
a: Sửa đề: 1/3^200
1/2^300=(1/8)^100
1/3^200=(1/9)^100
mà 1/8>1/9
nên 1/2^300>1/3^200
b: 1/5^199>1/5^200=1/25^100
1/3^300=1/27^100
mà 25^100<27^100
nên 1/5^199>1/3^300