( 5^{3 +} 5⁴ + 125²) : 5³

Bằng (5^{3 +} 5⁴ +5⁴):5³

bằng 1+5+5 bằng 11

\(a.a^5:a^2=a^6:a^2=a^{6-2}=a^4\)

= a⁶ : a²

= a^{6 - 2}

= a⁴

Trả lời :

16³ : 8⁴

= (2⁴)³ : (2³)⁴

= 2¹² : 2¹²

= 1

\(16^3:8^4\)

\(=\left(2^4\right)^3:\left(2^3\right)^4\)

\(=2^{12}:2^{12}\)

\(=1\)

3^2x+2 = 9^x+3

<=> 3^2x+2 = ( 3² )^x+3

<=> 3^2x+2 = 3^{2( x + 3 )} 

<=> 3^2x+2 = 3^2x+6

<=> 2x + 2 = 2x + 6

<=> 2x - 2x = 6 - 2

<=> 0x = 4 ( vô lí )

Vậy không có giá trị của x thỏa mãn

\(3^{2x+2}=9^{x+3}\)   

\(3^{2\left(x+1\right)}=9^{x+3}\)   

\(9^{x+1}=9^{x+3}\)   

\(x+1=x+3\) 

\(0=2\)  ( sai ) 

Vậy không có x thỏa mãn đề bài 

Bài 1 :

\(2^x.8=512\)

\(2^x=512:8\)

\(2^x=64\)

\(2^x=2^6\)

\(\Rightarrow x=6\)

\(b,\left(2x+1\right)^3=125\)

\(\left(2x+1\right)^3=5^3\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=2\)

\(c,x^{20}=x\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

\(d,\left(x-3\right)^{10}=0\)

\(\Rightarrow x-3=0\)

\(\Rightarrow x=3\)

a. 5³⁶ và 11²⁴

Ta có : 5³⁶ = ( 5³ )¹² = 125¹²

11²⁴ = ( 11² )¹² = 121¹²

Vì 125¹² > 121¹² 

nên 5³⁶ > 11²⁴

b. 32⁶⁰ và 81⁵⁰

Ta có : 32⁶⁰ = ( 2⁵ )⁶⁰ = 2³⁰⁰ = 8¹⁰⁰

81⁵⁰ = ( 3⁴ )⁵⁰ = 3²⁰⁰ = 9¹⁰⁰

Vì 8¹⁰⁰ < 9¹⁰⁰

nên 32⁶⁰ < 81⁵⁰

hỏi huốn  rose

\(a,2^{x+3}+2^x=144\)

\(2^x.2^3+2^x=144\)

\(2^x.\left(8+1\right)=144\)

\(2^x.9=144\)

\(2^x=16\)

\(2^x=2^4\)

\(\Rightarrow x=4\)

\(b,\left(2x+1\right)^2=81\)

\(\left(2x+1\right)^2=9^2\)

\(\Rightarrow\orbr{\begin{cases}2x+1=9\\2x+1=-9\end{cases}}\Rightarrow\orbr{\begin{cases}2x=8\\2x=-10\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=-5\end{cases}}\)

\(c,\left(7x-11\right)^3=2^5.5^2+200\)

\(\left(7x-11\right)^3=1000\)

\(\left(7x-11\right)^3=10^3\)

\(\Rightarrow7x-11=10\)

\(\Rightarrow7x=21\)

\(\Rightarrow x=3\)

a,\(2^{x+3}+2^x=144\)

\(2^x\left(2^3+1\right)=144\)

\(2^x.9=144\)

\(2^x=16\)

\(x=4\)

b,\(\left(2x+1\right)^2=81\)

\(\left(2x+1\right)^2=9^2\)

\(\Rightarrow\orbr{\begin{cases}2x+1=9\\2x+1=-9\end{cases}\Rightarrow\orbr{\begin{cases}x=4\\x=-5\end{cases}}}\)

c,\(\left(7x-11\right)^3=2^5.5^2+200\)

\(\left(7x-11\right)^3=1000\)

\(\left(7x-11\right)^3=10^3\)

\(7x-11=10\)

\(7x=21\)

\(x=3\)