1. 

a) 2ⁿ : 4 = 16

2ⁿ = 16.4

2ⁿ = 64

2ⁿ = 2⁶

=> n = 6

b) 5ⁿ = 625

5ⁿ = 5⁴

=> n = 4

c) 2ⁿ . 16 = 128

2ⁿ = 128 : 16

2ⁿ = 8

2ⁿ = 2³

=> n = 3

d) 3ⁿ⁺³ = 81

3ⁿ⁺³ = 3⁴

=> n + 3 = 4

=>      n = 4 - 3

=>      n = 1

1. 

a) 2ⁿ : 4 = 16

2ⁿ = 16.4

2ⁿ = 64

2ⁿ = 2⁶

=> n = 6

b) 5ⁿ = 625

5ⁿ = 5⁴

=> n = 4

c) 2ⁿ . 16 = 128

2ⁿ = 128 : 16

2ⁿ = 8

2ⁿ = 2³

=> n = 3

d) 3ⁿ⁺³ = 81

3ⁿ⁺³ = 3⁴

=> n + 3 = 4

=>      n = 4 - 3

=>      n = 1

2.

a) x³ = 64

x³ = 4³

=> x = 4

b) (2x + 1)³ = 27

(2x + 1)³ = 3³

2x + 1 = 3

2x = 3 - 1

2x = 2

=> x = 1

c) x³ = x 

=> x = {0;1}

d) 25 + 5x = 7⁵.7³

25 + 5x = 5764801

        5x = 5764801 - 25

        5x = 5764776

=> không có số tự nhiên x thoản mãn

a)

\(\Rightarrow3^{-2}.\left(3^3\right)^n=3^n\)

\(\Rightarrow3^{-2}.3^{3n}=3^n\)

\(\Rightarrow3^{3n-2}=3^n\)

\(\Rightarrow3n-2=n\)

\(\Rightarrow n=1\)

b)

\(\Rightarrow3^{4+n-2}=3^7\)

\(\Rightarrow x^{n+2}=3^7\)

\(\Rightarrow n+2=7\)

\(\Rightarrow n=5\)

c)

\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Rightarrow2^n.4,5=9.2^5\)

\(\Rightarrow2^n=2.2^5\)

\(\Rightarrow2^n=2^6\)

\(\Rightarrow n=6\)

d)

\(\Rightarrow\left(2^5\right)^{-n}.\left(2^4\right)^n=2048\)

\(\Rightarrow2^{n-5n}=2^{11}\)

\(\Rightarrow-4n=11\)

\(\Rightarrow n=-\frac{4}{11}\)

Cảm ơn bạn nhiều !!!

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

Bài 1:
a)1/9 x 27ⁿ= 3ⁿ

1/9=3ⁿ:27ⁿ

3ⁿ:27ⁿ=1/9

1ⁿ/9ⁿ=1/9

=>n=1

\(\frac{1}{2}.2^n+4.2^n=9.2^5\Rightarrow2^n\left(\frac{1}{2}+4\right)=288\Rightarrow2^n.\frac{9}{2}=288\Rightarrow2^{n-2}.9=288\Rightarrow2^{n-2}=32\)(dấu "=>" số 3 bn sửa thành 2^n-1.9=288=>2^n-1=32 nha)

=>2^n-1=2⁵=>n-1=5=>n=5+1=6

vậy......

~~~~~~~~~~~~~~~

mình có thể làm cho bạn thế này

Bé Kem

Số điểm xuất sắc: 123456789  - Điểm hỏi đáp 123456789 

a, 

5ⁿ + 5^{n + 2} = 650

=> 5ⁿ + 5ⁿ.5² = 650

=> 5ⁿ(1 + 5²) = 650

=> 5ⁿ.26 = 650

=> 5ⁿ = 25

=> n = 2

a) 5ⁿ +5ⁿ⁺² = 650

5ⁿ + 5ⁿ.5² = 650

5ⁿ.(1+25 ) = 650

5ⁿ.26= 650

5ⁿ = 25 = 5² 

=> n = 2

b) 3ⁿ⁺³ +5.3ⁿ = 864

3ⁿ.3³ +5.3ⁿ = 864

3ⁿ.(3³+5) = 864

3ⁿ.32 = 864

3ⁿ = 27 = 3³

=> n = 3

các bài cn lại bn dựa vào mak lm nha!
 

a. 

\(5^n+5^{n+2}=650\) 

\(5^n\left(1+5^2\right)=650\) 

\(5^n\left(1+25\right)=650\) 

\(5^n\cdot26=650\) 

\(5^n=650:26\) 

\(5^n=25\) 

\(5^n=5^2\Rightarrow n=2\) 

b. 

\(3^{n+3}+5\cdot3^n=864\) 

\(3^n\left(3^3+5\right)=864\) 

\(3^n\left(27+5\right)=864\) 

\(3^n\cdot32=864\) 

\(3^n=864:32\) 

\(3^n=27\) 

\(3^n=3^3\Rightarrow n=3\)

a) 5ⁿ + 5ⁿ⁺² = 650

=> 5ⁿ + 5ⁿ . 5² = 650

=> 5ⁿ (1 + 5²) = 650

=> 5ⁿ . 26 = 650

=> 5ⁿ = 25

=> n = 2

b) 3^{n+ 3} + 5.3ⁿ = 864

=> 3ⁿ . 3³ + 5.3ⁿ = 864

=> 3ⁿ(3³ + 5) = 864

=> 3ⁿ . 32 = 864

=> 3ⁿ = 27

=> n = 3