3:

a: 3^x*3=243

=>3^x=81

=>x=4

b; 2^x*16^2=1024

=>2^x=4

=>x=2

c: 64*4^x=16^8

=>4^x=4^16/4^3=4^13

=>x=13

d: 2^x=16

=>2^x=2^4

=>x=4

a)  1999^{2x - 6} = 1 

1999^{2x - 6} = 1999⁰

=>2x-6=0

2x=0+6

2x=6

x=6:2

x=3

b)  2^x x 4 = 128

2^x=128:4

2^x=32

2^x=2⁵

=>x=5

c)  ( 2x + 1 ) ³ = 125

( 2x + 1 ) ³ = 5³

2x+1=5

2x=5-1

2x=4

x=4:2

x=2

a)1999^2x-6=1

1999^2x-6=1999⁰

=>2x-6=0

2x=0+6

2x=6

x=6:2

x=3

b)2^x.4=128

2x=128:4

2x=32

x=32:2

x=5

c)(2x+1)³=125

(2x+1)³=5³

2x+1=5

2x=5-1

2x=4

x=4:2

x=2

a , x= 3                                       b , x = 5                                               c , x = 2

a) 2^x . 4 = 128

<=> 2^x = 32 

<=> 2^x = 2⁵

<=> x = 5

b) x¹⁵ = x¹

<=> x¹⁵ - x = 0

<=> x(x¹⁴ - 1) = 0

<=> \(\orbr{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x^{14}=1^{14}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)

c) (2x + 1)³ = 125

<=> (2x + 1)³ = 5³

<=> 2x + 1 = 5

<=> 2x = 4

<=> x = 2

d) (x - 5)⁴ = (x - 5)⁶

<=> (x - 5)⁶ - (x - 5)⁴ = 0

<=> (x - 5)⁴[(x - 5)² - 1] = 0

<=> \(\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2-1=0\end{cases}}\)

Khi (x - 5)⁴ = 0 => x - 5 = 0 => x = 5

Khi (x - 5)² - 1 = 0 <=> (x - 5)² = 1² <=> \(\orbr{\begin{cases}x-5=1\\x-5=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=6\\x=4\end{cases}}\)

a, 2x . 4 = 128

=> 2x = 128 : 4 = 32

=> x = 32 : 2 = 16

Vậy x = 16

b, x15 = x 1 => Sai đề

c, (2x + 1)³ = 125

=> ( 2x + 1 ) = 5³

=> 2x + 1 = 5 

=> 2x = 5 - 1

=> 2x = 4

=> x = 4 : 2

=> x = 2

Bài 3:

a) Ta có: \(2^x\cdot4=128\)

\(\Leftrightarrow2^x=32\)

hay x=5

Vậy: x=5

b) Ta có: \(2^x-26=6\)

\(\Leftrightarrow2^x=32\)

hay x=5

Vậy: x=5

c) Ta có: \(27\cdot3^x=3^7\)

\(\Leftrightarrow3^x=\frac{3^7}{27}=\frac{3^7}{3^3}=3^4\)

hay x=4

Vậy: x=4

d) Ta có: \(3^x=81\)

\(\Leftrightarrow3^x=3^4\)

hay x=4

Vậy: x=4

e) Ta có: \(64\cdot4^x=4^5\)

\(\Leftrightarrow4^3\cdot4^x=4^5\)

\(\Leftrightarrow4^{x+3}=4^5\)

\(\Leftrightarrow x+3=5\)

hay x=2

Vậy: x=2

g) Ta có: \(49\cdot7^x=2401\)

\(\Leftrightarrow7^2\cdot7^x=7^4\)

\(\Leftrightarrow7^{x+2}=7^4\)

\(\Leftrightarrow x+2=4\)

hay x=2

Vậy: x=2

h) Ta có: \(3^4\cdot3^x=3^7\)

\(\Leftrightarrow3^{x+4}=3^7\)

\(\Leftrightarrow x+4=7\)

hay x=3

Vậy: x=3

a) \(\left(x-1\right)^3=8=2^3\)

\(x-1=2\)

\(x=2+1=3\)

b) \(7^{2x-6}=49=7^2\)

\(2x-6=2\)

\(2x=6+2=8\)

\(x=8:2=4\)

c) \(\left(2x-14\right)^7=128=2^7\)

\(2x-14=2\)

\(2x=14+2=16\)

\(x=16:2=8\)

d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)

\(x=5\)

e) \(3\cdot\left(x+2\right):7\cdot4=120\)

\(x+2=120:3\cdot7:4\)

\(x+2=70\)

\(x=70-2=68\)

Lời giải:

a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$

$\Rightarrow x=3$

b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

c. $(2x-14)^7=128=2^7$

$\Rightarrow 2x-14=2$

$\Rightarrow 2x=16$

$\Rightarrow x=18$

d.

$x^4.x^5=5^3.5^6$

$x^9=5^9$

$\Rightarrow x=5$

e. 

$3(x+2):7=120:4=30$

$3(x+2)=30.7=210$

$x+2=210:3=70$

$x=70-2=68$

a ) 2^x . 4 = 128

2^x = 128 : 4

2^x = 32

2^x = 2⁵

=> x = 5

Vậy x = 5

b ) x¹⁵ = x

=> x¹⁵ : x = 1

x¹⁴ = 1

x¹⁴ = 1¹⁴

=> x = 1

Vậy x = 1

c ) ( 2x + 1 )³ = 125

( 2x + 1 )³ = 5³

=> 2x + 1 = 5

2x = 5 - 1

2x = 4

=> x = 4 : 2

x = 2

Vậy x = 2

d ) ( x - 5 )⁴ = ( x - 5 )⁶

( x - 5 )⁶ - ( x - 5 )⁴ = 0

( x - 5 )⁴ . [ ( x - 5 )² - 1 ] = 0

=> \(\orbr{\begin{cases}\left(x-5\right)^4=0\\\text{[}\left(x-5\right)^2-1=0\end{cases}}\)=> \(\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\)=> \(\orbr{\begin{cases}x=5\\x-5=1\end{cases}}\)=> \(\orbr{\begin{cases}x=5\\x=6\end{cases}}\)

Vậy x thuộc { 5 ; 6 }

a/ 2^x .4 =128

    2^x =128 : 4

    2^x = 32

     mak 2^4 =32      => x= 5

b/ x^15 = x

mak ta có 0 mũ bao nhiêu cx = 0 => x=0

c/ ( 2x + 1 )^3  = 125

mak 5^3 =125

ta có 2x + 1 = 5

    2x = 5 - 1

     2x = 4

       x = 4 : 2 = 2

a ) 2 ^x  . 4 = 128

    2 ^x          = 32

    2 ^x          = 2 ⁵

=> x = 5

b ) x ¹⁵ = x

=> x = 0 hoặc x = 1

c ) ( 2x + 1 ) ³ = 125

     ( 2x + 1 ) ³ = 5 ³

=> 2x + 1 = 5

     2x       = 4

       x       = 2

d ) ( x - 5 ) ⁴ = ( x - 5 ) ⁶

=> x - 5 = 0 hoặc x - 5 = 1

         x  = 5              x  = 6

Vậy x = 5 hoặc x = 6

a) x=5

b) x=1 hoặc x=0 hoặc x=-1

c) x=2

d) x=5 hoặc x=-4 hoặc x=6

a) \(2^x.4=128\)

\(2^x.2^2=2^7\)

\(2^x=2^7:2^2\)

\(2^x=2^5\)

\(x=5\)