\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot....\cdot\frac{30}{62}\cdot\frac{31}{64}=2^x\)

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot.....\cdot\frac{30}{31}\cdot\frac{31}{32}\right)=2^x\)

\(\Leftrightarrow\frac{1}{32}=2^{x+1}\)

Làm nốt.

ko làm được câu này hay câu b ib với tớ nha.khẳng định tối giải.

nham bang 4

hihi

\(\frac{4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)

\(\Rightarrow\frac{3\cdot2^{10}}{3^6}\cdot\frac{6^6}{2^6}=8^x\)

\(\Rightarrow\frac{4^5}{3^5}\cdot3^6=8^x\)

\(\Rightarrow4^5\cdot3=8^x\)

hình như sai đề hoặc mik làm sai:))

\(\frac{4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)

\(\frac{3\cdot4^5}{3\cdot3^5}\cdot\frac{6\cdot6^5}{2\cdot2^5}=8^x\)

\(\frac{4^5}{3^5}\cdot\frac{6^6}{2^5}=8^x\)

\(\left(\frac{4}{3}\right)^5\cdot\left(\frac{6}{2}\right)^6=8^x\)

\(\frac{4^5}{3^5}\cdot3^6=8^x\)

\(4^5\cdot3=8^x\)

\(1024\cdot3=8^x\)

\(3072=8^x\)

\(\Rightarrow\text{ }x\in\varnothing\)

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^{\left|2x+6\right|}\)

\(\Leftrightarrow\frac{4.\left(4^5\right)}{3.\left(3^5\right)}.\frac{6.\left(6^5\right)}{2.\left(2^5\right)}=8^{\left|2x+6\right|}\)

\(\Leftrightarrow\frac{4^6.6^6}{3^6.2^3}=8^{\left|2x+6\right|}\)

\(\Leftrightarrow\frac{\left(2^2\right)^6.\left(2.3\right)^6}{3^6.2^3}=8^{\left|2x+6\right|}\)

\(\frac{2^{12}.2^6.3^6}{3^6.2^3}=\frac{2^{18}.3^6}{3^6.2^3}=\frac{2^{15}.1}{1.1}=2^{15}=8^{\left|2x+6\right|}\)

=> 2¹⁵=(2³)^|2x+6|

2¹⁵=2^3|2x+6|

<=> 3|2x+6|=15

|2x+6|=15:3

|2x+6|=5

\(\Rightarrow\orbr{\begin{cases}2x+6=5\\2x+6=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{-11}{2}\end{cases}}\)

Bài 1:

\(A=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+1986}\right)\)

Nhận xét: \(1-\frac{1}{1+2+...+n}=1-\frac{2}{n\left(n+1\right)}=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n-1\right)\left(n+2\right)}{n\left(n+1\right)}\)

Do đó: \(\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+...+1986}\right)\)

\(=\frac{1\cdot4}{2\cdot3}\cdot\frac{2\cdot5}{3\cdot4}\cdot...\cdot\frac{1985\cdot1988}{1986\cdot1987}=\frac{1\cdot4\cdot1988}{1986\cdot3}=\frac{3976}{2979}\)

Bài 2:

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

\(\Rightarrow\frac{4\cdot4^5}{3\cdot3^5}\cdot\frac{6\cdot6^5}{2\cdot2^5}=2^x\)\(\Rightarrow\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=2^x\)

\(\Rightarrow\frac{\left(2^2\right)^6}{3^6}\cdot\frac{\left(2\cdot3\right)^6}{2^6}=2^x\)\(\Rightarrow\frac{2^{12}}{3^6}\cdot\frac{2^6\cdot3^6}{2^6}=2^x\)

\(\Rightarrow\frac{2^6\cdot3^6\cdot2^{12}}{2^6\cdot3^6}=2^x\)\(\Rightarrow2^{12}=2^x\Rightarrow x=12\)

đúng rồi đó bạn ks bạn ý đi chứ

chuẩn luôn

Theo đề bài ta có:
\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2x\)
\(\Leftrightarrow\frac{4^5\cdot4}{3^5\cdot3}\cdot\frac{6^5\cdot6}{2^5\cdot2}=2x\)
\(\Leftrightarrow\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=2x\)
\(\Leftrightarrow\left(\frac{4}{3}\cdot\frac{6}{2}\right)^6=2x\)
\(\Leftrightarrow4^6=2x\)
\(\Leftrightarrow2^{12}=2x\)
\(\Rightarrow x=2^{11}=2048\)

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)

\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)

\(\Rightarrow\frac{4^6}{3^6}.\frac{6^6}{2^6}=2^x\)

\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)

\(\Rightarrow\frac{\left(4.6\right)^6}{\left(3.2\right)^6}=2^x\)

\(\Rightarrow\frac{24^6}{6^6}=2^x\)

\(\Rightarrow4^6=2^x\)

\(\Rightarrow\left(2^2\right)^6=2^x\)

\(\Rightarrow2^{2.6}=2^x\)

\(\Rightarrow2^{12}=2^x\)

\(\Rightarrow x=12\)

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x.\)

\(\Rightarrow\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=2^x\)\(\Rightarrow\frac{4^6.6^6}{3^6.2^6}=2^x\)

\(\Rightarrow\frac{2^6.2^6.2^6.3^6}{3^6.2^6}=2^x\)\(\Rightarrow2^6.2^6=2^x\)

\(\Rightarrow2^{12}=2^x\Leftrightarrow x=12\)

b) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=\frac{4^5.\left(1+1+1+1\right)}{3^5.\left(1+1+1\right)}.\frac{6^5.\left(1+1+1+1+1+1\right)}{2^5.\left(1+1\right)}\)

                                                                                                       \(=\frac{4^5.4}{3^5.3}.\frac{6^5.6}{2^5.2}=\frac{4^6}{3^6}.\frac{6^6}{2^6}=\frac{2^{12}.2^6.3^6}{3^6.2^6}=2^{12}\)

   Ta có: \(2^{12}=\left(2^3\right)^4=8^4\)                                                    

Vậy x= 4

từ đầu bài sẽ ra:

(4^5*4)/(3^5.3)  .   (6^5.6)/(2^5.2)=8^x

4^6/3^6 . 6^6/2^6=8^x

4^6.6^6/3^6.2^6= 8^x

4^6.6^6/6^6=8^x

4^6=8^x

2^12=2^3x

3x=12

x=4

vậy x=4

nhìn hơi khó hiểu bạn thông cảm

\(=\frac{4\left(4^5\right)}{3\left(3^5\right)}.\frac{6\left(6^5\right)}{2^{10}}=8^x\)

\(=\frac{2^{12}}{3^6}.\frac{2^6.3^6}{2^{10}}\)= 8^x

\(=\frac{2^{18}.3^6}{3^6.2^{10}}\)= 8^x

\(=2^8=8^x\)

=> x vô nghiệm

Mk giải hơi bị ngắn nha1 Mong bạn hiểu XD

Hk tốt

\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)

\(=\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=8^x\)

\(=\frac{4^6.6^6}{3^6.2^6}=8^x\)

\(=\frac{4^6.6^6}{6^6}=8^x\)

\(=\frac{4^6.6^6}{4^6}=8^x\)

\(=2^{12}=2^{3x}\)

\(\Rightarrow3x=12\)

\(x=12\div3\)

\(x=4\)