Sửa đề:

\(7^{2x-6}=49\)

\(7^{2x-6}=7^2\)

\(\Rightarrow2x-6=2\)

\(2x=2+6\)

\(2x=8\)

\(x=8:2\)

\(x=4\)

7^{2x - 6} = 49

7^{2x - 6} = 7² (cùng cơ số)

⇒ 2x - 6 = 2

2x = 2 + 6

2x = 8

x = 8 : 2

x = 4

Lời giải:

\(\frac{6^{x+3}-6^{x+1}+6^x}{211}=\frac{7^{2x}+7^{2x+1}+7^{2x-3}}{8\frac{1}{49}}\)

\(\Leftrightarrow \frac{6^x(6^3-6+1)}{211}=\frac{7^{2x}(1+7+\frac{1}{7^3})}{\frac{393}{49}}\)

\(\Leftrightarrow 6^x=7^{2x}.\frac{915}{917}\)

\(\Leftrightarrow (\frac{6}{49})^x=\frac{915}{917}\)

\(\Rightarrow x=\log_{\frac{6}{49}}\frac{915}{917}\)

@Trần Thanh Phương

giúp đc k ạ :3?

Thầy Akai Haruma em hơi thắc mắc dòng cuối thầy ghi là log :<?

Nghĩa là j ạ :<? mong thầy giải cách dễ hơi ạ :V

\(\left(x-1\right)^2=1\\ \Rightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\\ 7^{2x-6}=49\\ \Rightarrow7^{2x-6}=7^2\\ \Rightarrow2x-6=2\\ \Rightarrow2x=8\\ \Rightarrow x=4\)

b: =>2x-6=2

hay x=4

\(a,\left(x-1\right)^2=1\\ \Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\\ b,7^2x-6=49\\ \Leftrightarrow49x=55\\ \Leftrightarrow x=\dfrac{55}{49}\)

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. 

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

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

$x+2=210:3=70$

$x=70-2=68$

1: =>(x+3)(x-5)=0

=>x=5 hoặc x=-3

2: =>(x-1)(5x-1)=0

=>x=1/5 hoặc x=1

5: =>(x-4)*x=0

=>x=0 hoặc x=4

10: =>(x+5)(x-3)=0

=>x=3 hoặc x=-5

9: =>(x-2)(x-4)=0

=>x=2 hoặc x=4

7: =>(x-6)(2x-1)=0

=>x=1/2 hoặc x=6

8: =>(2x-1)(3x-12)=0

=>x=4 hoặc x=1/2

a) (x - 1)² = 1.

<=> x - 1 = 1 hoặc x - 1 = -1.

<=> x = 2 hoặc x = 0.      

b) 7^{2x - 6} = 49.

<=> 7^{2x - 6} = 7².   

<=> 2x - 6 = 2.

<=> x = 4.  

c) (2x - 16)⁷ = 128.

<=> (2x - 16)⁷ = 2⁷.

<=> 2x - 16 = 2.

<=> x = 9.