71⁵⁰<81⁵⁰=3²⁰⁰

37⁷⁵>27⁷⁵=3²²⁵

vậy 71⁵⁰<81⁵⁰<27⁷⁵<37⁷⁵

\(71^{50}< 81^{50}=3^{200}\)

\(37^{75}>27^{75}=3^{225}\)

vì \(71^{50}< 3^{200}< 3^{225}< 37^{75}\)=>\(71^{50}< 37^{75}\)

( x + 15 ) : 3 = 1

x + 15 = 1/ 3

x = -44 / 3

tk nha

\(\left(x+15\right):3=1\)

\(x+15=3\)

\(x=12\)

A=3^1+3^2+...+3^2016       (1)

3A=3^2+3^3+....+3^2017     (2)

TRỪ VẾ VỚI VẾ CỦA (2) CHO (1)

3A-A=(3^2+3^3+...+3^2017)-(3^1+3^2+...+3^2016)

2A=3^2017-3

2A+3=3^2017

TA CÓ 2A+3=3^x

=>x=2017

=>

\(A=3^1+3^2+3^3+...+3^{2016}\)

\(3A=3^2+3^3+3^4+...+3^{2017}\)

1220 nha

2.(21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40)=1220

5^2x-3.2.25=625.3

5^2x-3.50=1875

5^2x-3=75/2

=> x ko có gia trị

X⁵⁰= x

3.2^x=768

  2^x=768:3

  2^x=256

   2^x=2^8

chúc bn hk tốt ~~~

2^x = 768 ÷ 3 

2^x = 256

2^x = 2^8

X = 8

2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰

vì 8<9 => 8¹⁰⁰<9¹⁰⁰

=> 2³⁰⁰<3²⁰⁰

Chúc bạn học tốt!

\(2^{300}=\left(2^3\right)^{100}\)=8^100

\(3^{200}=\left(3^2\right)^{100}\)=9^100

vì 8^100 < 9^100 => 2^300 < 3^200

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+....+\left(2^9+2^{10}\right)\)

\(=2.\left(1+2\right)+2^3.\left(1+2\right)+...+2^9.\left(1+2\right)\)

\(=2.3+2^3.3+...+2^9.3\)

\(=3.\left(2+2^3+...+2^9\right)⋮3\)