1) \(2^{x+1}\cdot2^{2014}=2^{2015}\)\(\Leftrightarrow2^{2014x+2014}=2^{2015}\)\(\Leftrightarrow2014x+2014=2015\)\(\Leftrightarrow x=\frac{1}{2014}\)

2) \(7x-2x=\frac{6^{17}}{6^{15}}+\frac{44}{11}\)\(\Leftrightarrow5x=6^2+4=36+4=40\)\(\Leftrightarrow x=\frac{40}{5}=8\)

3) \(3^x=9\)\(\Leftrightarrow3^x=3^2\)\(\Leftrightarrow x=2\)

4) \(7x-x=\frac{5^{21}}{5^{19}}+3\cdot2^2-7^0\)\(\Leftrightarrow6x=5^2+3\cdot4-1=25+12-1=36\)\(\Leftrightarrow x=6\)

5) \(4^x=64\)\(\Leftrightarrow4^x=4^3\)\(\Leftrightarrow x=3\)

6) \(9^{x-1}=9\)\(\Leftrightarrow x-1=1\)\(\Leftrightarrow x=0\)

7) \(\frac{2^x}{2^5}=1\)\(\Leftrightarrow2^{x-5}=2^0\)\(\Leftrightarrow x-5=0\)\(\Leftrightarrow x=5\)

8) \(\left(5x-9\right)^3=216\)\(\Leftrightarrow\left(5x-9\right)^3=6^3\)\(\Leftrightarrow5x-9=6\)\(\Leftrightarrow5x=15\)\(\Leftrightarrow x=3\)

9) \(5\cdot3^{7x-11}=135\)\(\Leftrightarrow5.3^{7x-11}=5.3^3\)\(\Leftrightarrow3^{7x-11}=3^3\)\(\Leftrightarrow7x-11=3\)\(\Leftrightarrow7x=14\Leftrightarrow x=2\)

10) \(2.3^x=19\cdot3^8-81^2\)\(\Leftrightarrow2.3^x=19\cdot3^8-3^8=18.3^8=2.3^{11}\)\(\Leftrightarrow3^x=3^{11}\Leftrightarrow x=11\)

Đây là cách làm của mình. Bạn có thể chỉnh sửa tuỳ ý theo cách làm của bạn nhé ^^

Học tốt ^3^

a) (2⁴⁷ x 5¹⁴ x 2¹³ x 9¹³ x 5¹⁷ x 9¹⁷ ) : (2³⁰ x 2³⁰ x 5³⁰ x 9³⁰)

(2⁶⁰ x 5³¹ x 9³⁰) : (2⁶⁰ x 5³⁰ x 9³⁰) = 5

mòi tay không

Học thì sao phải mỏi tay

a, A= 5x4¹⁵ x 9⁹ - 4x3²⁰x 8⁹ = 5x2³⁰x3¹⁸-2²x 2²⁷x3²⁰

=2²⁹x3¹⁸(2x5-3²)=2²⁹x3¹⁸

B=5x2⁹x6¹⁹-7x2²⁹x27⁶=5x2⁹x2¹⁹x3¹⁹7x2²⁹x3¹⁸

=2³⁸x3¹⁸(5x3-7x2)=2²⁸-3¹⁸

^->A:B= 2²⁹x3¹⁸:2²⁸:3¹⁸=2

b sai nha

Bài 1 câu a:

1/-8 + -5/8

= -1/8 - 5/8

= -6/8

= -3/4

Câu b:

-1/21 + -1/28

= -4/84 - 3/84

= - 7/854

Câu c:

-5/9 + 8/15 + -2/11 + 4/-9 + 7/15

= (8/15+ 7/15) - (5/9 + 4/9) - 2/11

= 1 - 1 - 2/11

= 0 - 2/11

= - 2/11

Câu d:

-25/-75 + 17/34 + 121/- 132

= 1/3 + 1/2 - 11/12

= 4/12 + 6/12 - 11/12

= 10/12 - 11/12

= - 1/12

Bài 2a:

51/23 = 5151/2323 = 515151/232323

\(\frac{5151}{2323}\) = \(\frac{5151:101}{2323:101}\) = \(\frac{51}{23}\) (1)

\(\frac{515151}{232323}\) = \(\frac{515151:10101}{232323:10101}\) = \(\frac{51}{23}\) (2)

Từ (1) và (2) ta có:

\(\frac{51}{23}=\frac{5151}{2323}=\frac{515151}{232323}\) (đpcm)