a: \(\Leftrightarrow4^x\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)=4^8\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)\)

=>4^x=4^8

=>x=8

b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)

=>2^x=2^11

=>x=11

c: =>1/6*6^x+6^x*36=6^15(1+6^3)

=>6^x=6*6^15

=>x=16

d: \(\Leftrightarrow8^x\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)=8^9\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)\)

=>x=9

Bài 1: 

a: \(=\dfrac{-1}{8}+1-\dfrac{9}{4}-1\)

\(=\dfrac{-1}{8}-\dfrac{18}{8}=\dfrac{-19}{8}\)

b: \(=4\cdot1-2\cdot\dfrac{1}{4}+3\cdot\dfrac{-1}{2}+1\)

\(=4-\dfrac{1}{2}-\dfrac{3}{2}+1\)

=5-2

=3

a.\(3^{x-1}=243\)

\(3^x:3^1=243\)

\(3^x=729\)

\(\Leftrightarrow3^6=729\)

\(\Leftrightarrow x=6\)

b.\(\left(\dfrac{2}{3}\right)^{x+1}=\dfrac{8}{4}\)

\(\left(\dfrac{2}{3}\right)^x.\left(\dfrac{2}{3}\right)=\dfrac{8}{4}\)

\(\left(\dfrac{2}{3}\right)^x=3\)

Câu b tính đến đây rồi không mò đc x nữa.

Câu c:

3\(^{x}\) + 3\(^{x+2}\) = 270

3\(^{x}\).(1 + 3\(^2\)) = 270

3\(^{x}\).(1+ 9) = 270

3\(^{x}\).10 = 270

3\(^{x}\) = 270 : 10

3\(^{x}\) = 27

3\(^{x}\) = 3\(^3\)

\(x=3\)

Vậy \(x=3\)

a)\(\left(\dfrac{1}{2}\right)^n=\dfrac{1}{32}\)

=>\(\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{2}\right)^5\)

=>n=5

b)\(\left(\dfrac{343}{125}\right)=\left(\dfrac{7}{5}\right)^n\)

=>\(\left(\dfrac{7}{5}\right)^3=\left(\dfrac{7}{5}\right)^n\)

=>n=3

c)\(\dfrac{16}{2^n}=2\)

=>2ⁿ=\(\dfrac{16}{2}\)

=>2ⁿ=8

=>2ⁿ=2³

=>n=3

d)\(\dfrac{\left(-3\right)^n}{81}=-27\)

=>(-3)ⁿ=-27.81

=>(-3)ⁿ=-2187

=>(-3)ⁿ=(-3)⁷

=>n=7

e)8ⁿ:2ⁿ=4

=>(2³)ⁿ:2ⁿ=4

=>2³ⁿ:2ⁿ=4

=>2^3n-n=4

=>2²ⁿ=4

=>2²ⁿ=2²

=>2n=2

=>n=1

f)3².3ⁿ=3⁵

=>3ⁿ=3⁵:3²

=>3ⁿ=3^5-2

=>3ⁿ=3³

=>n=3

g) (2²:4).2ⁿ=4

=>1.2ⁿ=2²

=>n=2

h)3^-2.3⁴.3ⁿ=3⁷

=>\(\left(\dfrac{1}{3}\right)^2\).3⁴.3ⁿ=3⁷

=>3².3ⁿ=3⁷

=>3²⁺ⁿ=3⁷

=>2+n=7

=>n=5

b) \(\dfrac{7}{15}-\dfrac{9}{19}\)\(-\dfrac{-8}{15}-\dfrac{10}{19}\)
=\(\left(\dfrac{7}{15}-\dfrac{8}{15}\right)\) \(-\left(\dfrac{9}{19}-\dfrac{10}{19}\right)\)
= \(-\dfrac{1}{15}\) - \(\left(-\dfrac{1}{19}\right)\)
\(=-\dfrac{1}{15}\) + \(\dfrac{1}{19}\)

= \(-\dfrac{4}{285}\)

c) \(1\dfrac{1}{3}\) \(\div\) \(\dfrac{4}{5}\) + 2\(\dfrac{2}{3}\) \(\div\)\(\dfrac{4}{5}\)
= \(\left(1\dfrac{1}{3}+2\dfrac{2}{3}\right)\) \(\div\dfrac{4}{5}\)
= \(\left[\left(1+2\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\right]\) \(\div\dfrac{4}{5}\)
= ( 3 + 1 ) \(\div\dfrac{4}{5}\)
= 4 \(\div\dfrac{4}{5}\)
= \(\dfrac{4.5}{4}\)
= 5

1) Tính

a) 25³ : 5² = (5²)³ : 5² = 5⁶ : 5² = 5⁴ = 625

\(b)\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^6=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^6=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^9\) d) 9 . 3² . \(\dfrac{1}{81}\) . 3² = 3² . 3² . \(\dfrac{1}{3^4}\) . 3² = 9

2) Tìm x thuộc Q, biết:

a) 3^{x + 2} = 27

=> 3^{x + 2} = 3³

x + 2 = 3

x = 3 - 2

x = 1

b) \(\left(\dfrac{1}{2}x-3\right)^4=81\)

\(\Rightarrow\left(\dfrac{1}{2}x-3\right)^4=3^4\)

\(\dfrac{1}{2}x-3=3^{ }\)

\(\dfrac{1}{2}x=3+3\)

\(\dfrac{1}{2}x=9\)

\(x=9:\dfrac{1}{2}\)

\(x=18\)

c) \(\left(x-\dfrac{1}{2}\right)^3=-27\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(-3\right)^3\)

\(x-\dfrac{1}{2}=-3\)

\(x=-3+\dfrac{1}{2}\)

\(x=\dfrac{-5}{2}\)

d) 5 . 5^{x + 1} = 125

5^{x + 1} = 125 : 5

5^{x + 1} = 25

5^{x + 1} = 5²

x + 1 = 2

x = 2 - 1

x = 1.

1: \(=\dfrac{3}{4}+\dfrac{5}{4}\cdot\dfrac{8}{3}-\dfrac{1}{4}\cdot\dfrac{5}{6}=\dfrac{3}{4}+\dfrac{10}{3}-\dfrac{5}{24}\)

\(=\dfrac{18}{24}+\dfrac{80}{24}-\dfrac{5}{24}=\dfrac{93}{24}=\dfrac{31}{8}\)

2: \(=\left(7+\dfrac{23}{27}-\dfrac{23}{27}\right)+\left(\dfrac{11}{25}+\dfrac{14}{25}\right)+3.25\)

\(=7+1+3.25=8+3.25=11.25\)

3: \(=\left(\dfrac{1}{9}\cdot9\right)^{2005}-4^2=1-16=-15\)

4: \(=2\cdot\dfrac{9}{4}-\dfrac{7}{2}=\dfrac{9}{2}-\dfrac{7}{2}=1\)

5: \(=\dfrac{15}{2}\cdot\dfrac{-3}{5}+\dfrac{5}{2}\cdot\dfrac{-3}{5}=\dfrac{-3}{5}\cdot\left(\dfrac{15}{2}+\dfrac{5}{2}\right)=\dfrac{-3}{5}\cdot10=-6\)

6: \(=\left(\dfrac{6}{10}+\dfrac{5}{10}\right)^2=\left(\dfrac{11}{10}\right)^2=\dfrac{121}{100}\)

7: \(=\dfrac{1}{2}\cdot\dfrac{-7}{2}=\dfrac{-7}{4}\)

a, \(\left(\dfrac{2}{3}\right)^3=\dfrac{2^3}{3^3}=\dfrac{8}{27}\)

\(b,\left(-2\dfrac{3}{4}\right)^2=\left(-\dfrac{11}{4}\right)^2=\dfrac{-11^2}{4^2}=\dfrac{121}{16}\)

c,\(\left(0,6\right)^4=\left(\dfrac{6}{10}\right)^4=\left(\dfrac{3}{5}\right)^4=\dfrac{3^4}{5^4}=\dfrac{81}{625}\)

d, \(\left(-\dfrac{1}{2}\right)^4=-\dfrac{1^4}{2^4}=\dfrac{1}{16}\)

e, \(\left(-\dfrac{1}{2}\right)^5=-\dfrac{1^5}{2^5}=-\dfrac{1}{32}\)

a) 27^x : 3^x = 9

(27 : 3)^x = 9

9^x = 9¹

x = 1

b) 25 : 5^x =5

5^x = 25 : 5

5^x = 5¹

x = 1

c) 2 : (x + 2)² = \(\dfrac{1}{18}\)

(x + 2)² = 2 : \(\dfrac{1}{18}\)

(x + 2)² = 36

\(\Rightarrow\left[{}\begin{matrix}x+2=6\\x+2=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)

d) (5x - 1)² = \(\dfrac{36}{49}\)

(5x - 1)² = \(\left(\dfrac{6}{7}\right)^2\)

Bạn làm tiếp nha, mình có việc bận :v