Bài 9: Thứ tự thực hiện các phép tính. Luyện tập

\(\left(5x-2\right).6^3=3.6^5\)

( 5x -2 ) .216 = 23 328

5x - 2 = 23 328 : 216

5x -2 = 108

5x = 108 + 2

5x = 110

x = 110 : 5

x = 22

Vậy x = 22

( 5x - 2 ) . \(6^3\) = 3. \(6^5\)

=> ( 5x - 2 ). 216= 23328

=> ( 5x - 2 ) = 23328 : 216

=> ( 5x - 2) = 108

=> 5x = 108 + 2

=> 5x = 110

=> x = 110 : 5

=> x = 22

Vậy x = 22

\((5x−2)6^3=3.6^5\)

\(\text{(5x - 2)216 = 23328}\)

\(\text{5x - 2 = 23 328 : 216}\)

\(\text{5x -2 = 108}\)

\(5x = 108 + 2\)

\(5x = 110\)

\(x = 110 : 5\)

\(x = 22\)

\(\Rightarrowđpcm\)

\(3^3.5^3-20.\left\{300-\left[546-2^3.\left(7^8:7^6+7^0\right)\right]\right\}\)

= \(27.125-20.\left\{300-\left[546-8.50\right]\right\}\)

= \(3375-20.\left\{300-\left[546-400\right]\right\}\)

= \(3375-20.\left\{300-146\right\}\)

= \(3375-20.154=3375-3080=295\)

Đáp án hoàn toàn chính xác đấy.

Chúc bạn học tốt :))

3³.5³-20.{ 300-[ 546-2³.(7⁸:7⁶+7⁰)]}

=-98-20.{300- [546-8.50]}

=-98-20.{300-[546-400]}

=-98-20.{300-146}

=-98-20.154

=-3178

Chúc bạn học tốt Khanh Nhí

\(=\)\(3^3.5^3-20.\left\{300-\left[546-2^3.\left(7^8:7^6+7^0\right)\right]\right\}\)

\(=\)\(27.125-20.\left\{300-\left[546-2^3.\left(49+1\right)\right]\right\}\)

\(=\)\(3375-20.\left\{300-\left[546-8.50\right]\right\}\)

\(=3375-20\left(300-146\right)\)

\(=3375-20.154\)

\(=3375-3080\)

\(=295\)

câu này giống câu dưới mà Khanh Nhí

3³.5³-20.{300-[546-2³.(7⁸:7⁶+7⁰)]}

= 3³.5³-20.{300-[546-2³.(7²+1)]}

= 3³.5³-20.[300-(546-2³.50)]

= 3³.5³-20.[300-(546-400)]

= 3³.5³-20.(300-146)

= 3³.5³-20.154

= 3375-3080

= 295.

(3x - 48). 6 = 3⁶ + 4 -135

(3x - 48) . 6 = 598

3x - 48 = 598 : 6 = 99,6

3x = 147,6

x = 49,2

(3x-48).6=3³.3³+2²+3²-12²

(3x-48).6=3⁶+4+9-144

(3x-48).6=729-131

(3x-48).6=598

3x-48=598:6

3x-48=\(\dfrac{299}{3}\)
3x=\(\dfrac{299}{3}\)+48

3x=\(\dfrac{443}{3}\)

\(\Leftrightarrow x=\dfrac{443}{9}\)

(3.x-48).6=3³.3³+2²+3²-12²

(3.x-48).6=27.27+4+9-144

(3.x-48).6=729+13-144

(3.x-48).6= 598

(3.x-48)=598:6

3.x-48=\(\dfrac{299}{3}\)

3x = \(\dfrac{443}{3}\)

=>x=\(\dfrac{443}{9}\)

Chúc bạn học tốt

\(\left(3x-4x\right)\cdot6=3^3\cdot3^3+2^3+3^2-12^2\)

\(\Leftrightarrow18x-288=3^6+2^3+3^2-12^2\)

\(\Leftrightarrow18x-288=729+8+\left(3-12\right)\cdot\left(3+12\right)\)

\(\Leftrightarrow18x-288=729+8+\left(-9\right)\cdot15\)

\(\Leftrightarrow18x-288=729+8-135\)

\(\Leftrightarrow18x-288=602\)

\(\Leftrightarrow18x=602+288\)

\(\Leftrightarrow18x=890\)

\(\Rightarrow x=\dfrac{445}{9}\)

Vậy \(x=\dfrac{445}{9}\)

(3x-48).6=3³.3³+2³+3²-12²

(3x-48).6=3⁶+8+9-144

(3x-48).6=729+-127

(3x-48).6= 602

3x-48=\(\dfrac{602}{6}\)

3x=\(\dfrac{602}{6}\)+48

3x=\(\dfrac{445}{3}\Leftrightarrow x=\dfrac{445}{9}\)

\(19,8:0,25.7,2:0,125.8,4:0,5\)

\(=19,8.4.7,2.8.8,4.2\)

\(=79,2.57,6.16,8\)

\(=76640,256\)

\(6,6.8.2,4.4.16,8:0,2\)

\(=52,8.9,6.84\)

\(=42577,92\)

a) $19,8:0,25.7,2:0,125.8,4:0,5$

$=19,8:\dfrac{1}{4}.7,2:\dfrac{1}{8}.8,4:\dfrac{1}{2}$

$=19,8.4.7,2.8.8,4.2=76640,256$

b) $6,6.8.2,4.4.16,8:0,2$

$=6,6.8.2,4.4.16,8:\dfrac{1}{5}$

$=6,6.8.2,4.4.16,8.5=42577,92$

Quy ước toán học dấu x = dấu .

===================================

1. (3^x - 5)⁴ = 2⁸

<=> (3^x - 5)⁴ = 4⁴

=> Ta có 2 trường hợp :

* TH1 : \(3^x-5=4\Rightarrow3^x=9\Rightarrow x=2\)

* TH2 : \(3^x-5=-4\Rightarrow3^x=1\Rightarrow x=0\)

Vậy x=1 hoặc x=0

a, \(\left(3^x-5\right)^4=2^8\)

\(\Rightarrow\left(3^x-5\right)^4=\left(2^2\right)^4\)

\(\Rightarrow\left(3^x-5\right)^4=4^4\)

\(\Rightarrow3^x-5=4\Rightarrow3^x=1=3^0\)

\(\Rightarrow x=0\)

b, \(3^{x+2}+3^x=10^2-10\)

\(\Rightarrow3^x.\left(3^2+1\right)=100-10\)

\(\Rightarrow3^x.10=90\Rightarrow3^x=9=3^2\)

\(\Rightarrow x=2\)

c, \(3^{x+1}-3^x=4.5-2\)

\(\Rightarrow3^x.\left(3-1\right)=20-2\)

\(\Rightarrow3^x.2=18\Rightarrow3^x=9=3^2\)

\(\Rightarrow x=2\)

Chúc bạn học tốt!!! Mấy câu còn lại làm tương tự!

1) \(\left(3^x-5\right)^4=2^8\)

\(\Leftrightarrow\left[{}\begin{matrix}3^x-5=4\\3^x-5=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3^x=9\\3^x=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3^x=3^3\\3^x=3^0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)

Vậy \(x_1=0;x_2=3\)

b) \(3^{x+2}+3^x=10^2-10\)

\(\Leftrightarrow\left(3^2+1\right)\cdot3^x=100-10\)

\(\Leftrightarrow\left(9+1\right)\cdot3^x=90\)

\(\Leftrightarrow3^x=9\)

\(\Leftrightarrow3^x=3^2\)

\(\Leftrightarrow x=2\)

Vậy \(x=2\)

c) \(3^{x+1}-3^x=4\cdot5-2\)

\(\Leftrightarrow\left(3-1\right)\cdot3^x=20-2\)

\(\Leftrightarrow2\cdot3^x=18\)

\(\Leftrightarrow3^x=9\)

\(\Leftrightarrow3^x=3^2\)

\(\Leftrightarrow x=2\)

Vậy \(x=2\)

d) \(5^{x+2}-5^x=10^3:2+10^2\)

\(\Leftrightarrow\left(5^2-1\right)\cdot5^x=1000:2+100\)

\(\Leftrightarrow\left(25-1\right)\cdot5^x=500+100\)

\(\Leftrightarrow24\cdot5^x=600\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow5^x=5^2\)

\(\Leftrightarrow x=2\)

Vậy \(x=2\)

e) \(4^x+4^{x-1}=84:7\)

\(\Leftrightarrow\left(4+1\right)\cdot4^{x-1}=12\)

\(\Leftrightarrow5\cdot4^{x-1}=12\)

\(\Leftrightarrow4^{x-1}=\dfrac{12}{5}\)

giải tiếp...

\(B=12.10^8+17.10^7+5.10^4+3\)

\(B=12.10^4.10^4+17.10^4.10^3+5.10^4+3\)

\(B=12.10000.10^4+17.1000.10^4+5.10^4+3\)

\(B=120000.10^4+17000.10^4+5.10^4+3\)

\(B=(120000+17000+5).10^4+3\)

\(B=137005.10^4+3\)

\(B=137005.10000+3\)

\(B=1370050003\)

\(B=12\cdot10^8+17\cdot10^7+5\cdot10^4+3\)

\(=12\cdot10^8+17\cdot10^7+5\cdot10000+3\)

\(=12\cdot10^8+17\cdot10^7+50000+3\)

\(=12\cdot10^8+17\cdot10^7+50003\)

Ta có :

Lũy thừa các số có tận cùng là chữ số 5 sẽ tận cùng là 5

Do đó :

\(2.5^y=\left(....0\right)\Rightarrow35^x+9=\left(....0\right)\)

\(\Rightarrow35^x=\left(...1\right)\)

\(\Rightarrow x=0\)

\(\Rightarrow2.5^y=10\)

\(\Rightarrow y=1\)

Vậy cặp giá trị (x,y) cần tìm là (0,1)

1. Ta có: \(16^{30}=\left(2^4\right)^{30}=2^{120}\)

Mà \(2^{120}< 3^{120}< 3^{121}\)

\(\Rightarrow2^{120}< 3^{121}\)

\(\Rightarrow16^{30}< 3^{121}\)

2. Ta có: \(5^{22}=5^{2.11}=\left(5^2\right)^{11}=25^{11}\)

Vì 25 < 64 nên \(25^{11}< 64^{29}\)

Vậy \(5^{22}< 64^{29}\)

3. Ta có: \(8^{120}=\left(2^3\right)^{120}=2^{360}\)

\(64^{29}=\left(2^6\right)^{29}=2^{174}\)

Vì 360 < 174 nên \(2^{360}< 2^{174}\)

Vậy \(8^{120}>64^{29}\)

4. Ta có: \(333^{444}=\left(333^4\right)^{111}\) \(=\left(111^4.3^4\right)^{111}=\left(111^4.81\right)^{111}\)

\(444^{333}=\left(444^3\right)^{111}\) \(=\left(111^3.4^3\right)^{111}=\left(111^3.64\right)^{111}\)

Vì \(111^4.81>111^3.64\) nên \(\left(111^4.81\right)^{111}>\left(111^3.64\right)^{111}\)

Vậy \(333^{444}>444^{333}\)