a)Ta có:

\(2^{24}=\left(2^6\right)^4=64^4\)

\(3^{16}=\left(3^4\right)^4=81^4\)

Vì 64⁴<81⁴ nên 2²⁴<3¹⁶

b)Ta có:

\(2^{30}=\left(2^3\right)^{10}=8^{10}\)

\(3^{20}=\left(3^2\right)^{10}=9^{10}\)

Vì 8¹⁰<9¹⁰ nên 2³⁰<3²⁰

a, 2²⁴ = 2^3.8 = (2³)⁸ = 8⁸

    3¹⁶ = 3^2.8 = (3²)⁸ = 9⁸

Có 8⁸ < 9⁸

=> 2²⁴ < 3¹⁶

b, 2³⁰ = 2^3.10 = (2³)¹⁰ = 8¹⁰

   3²⁰ = 3^2.10 = (3²)¹⁰ = 9¹⁰

Vì 8¹⁰ < 9¹⁰

=> 2³⁰ < 3²⁰

a, (2x-3)³ = -64

=> (2x-3)³ = -4³

=> 2x-3=-4

=> 2x = -1

=> x = -1 : 2

=> x = -1/2

b, (2x-3)² =25

=>  (2x-3)² =5^2

=> 2x-3 = 5

=> 2x = 8

=> x = 4

c, (3x-4)² =36

=> (3x-4)² =6²

=> 3x-4 = 6

=> 3x = 10

=> x = 3.(3)

d, 2^x+1 = 64

=> 2^x+1  = 2⁶

=> x+1 = 6

=> x = 5

a/ (2x - 3)³ = -64 => (2x - 3)³ = (-4)³ =>  2x - 3 = -4 => 2x = -1 => x = -1/2

b/ (2x - 3)² = 25 => (2x - 3)² = 5² => 2x - 3 = 5 => 2x = 8 => x = 4

c/ (3x - 4)² = 36 => (3x - 4)² = 6² => 3x - 4 = 6 => 3x = 10 => x = 10/3

d/ 2^x+1 = 64 => 2^x+1 = 2⁶ => x + 1 = 6 => x = 5

\(C=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{2016}}\)

\(\Rightarrow4C=4+1+\frac{1}{4}+...+\frac{1}{4^{2015}}\)

\(\Rightarrow4C-C=3C=4-\frac{1}{4^{2015}}\)

\(\Rightarrow C=\left(\frac{4^{2016}-1}{4^{2015}}\right):3=\frac{4^{2016}-1}{4^{2015}.3}\)

\(C=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{2016}}\)

\(4C=4+1+\frac{1}{4^2}+...+\frac{1}{4^{2015}}\)

\(3C=4C-C=4-\frac{1}{4^{2016}}\)

=> \(C=\frac{4-\frac{1}{4^{2016}}}{3}\)

\(a^2+b^2+c^2\ge ab+bc+ca\\ =>2a^2+2b^2+2c^2\ge2ab+2bc+2ca\)

\(=>2a^2+2b^2+2c^2-2ab-2bc-2ca\ge0\)

\(=>a^2-2ab+b^2+b^2-2bc+c^2+c^2-2ac+a^2\ge0\)

\(=>\left(a-b\right)^2+\left(b-a\right)^2+\left(c-a\right)^2\ge0\)(đúng)

Dấu "=" xảy ra khi : \(\hept{\begin{cases}a-b=0\\b-c=0\\c-a=0\end{cases}\Rightarrow\hept{\begin{cases}a=b\\b=c\\c=a\end{cases}\Rightarrow}a=b=c}\)

Chúc bạn học tốt nhé

 T I C K ủng hộ nha

\(\)

Ta có: \(\frac{a}{b}=\frac{10}{3}\Rightarrow a=\frac{10}{3}b\)

Thay vào A ta được: \(A=\frac{3\left(\frac{10}{3}b\right)-2b}{\frac{10}{3}b-3b}=\frac{10b-2b}{\frac{1}{3}b}=\frac{8b}{\frac{1}{3}b}=24\)

                                       Vậy A = 24

a) x³ = -8

x³ = (-2)³

Vậy x = -2

b) ( x + 5 )³ = -27

( x + 5 )³ = (-3)³

x + 5 = -3

x = -8