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13 tháng 7 2023
Sửa đề: 3^5+3^5+3^5; 2^x
=>\(2^x=\dfrac{4^5\cdot4}{3^5\cdot3}\cdot\dfrac{6^5\cdot6}{2^5\cdot2}\)
=>\(2^x=\left(\dfrac{4}{3}\right)^6\cdot\left(\dfrac{6}{2}\right)^6=4^6=2^{12}\)
=>x=12
DX
6 tháng 8 2021
\(\dfrac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\dfrac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^n\)
\(\Rightarrow\dfrac{4^5.4}{3^5.3}.\dfrac{6^5.6}{2^5.2}=2^n\)
\(\Rightarrow\dfrac{4^5.4.6^5.6}{3^5.3.2^5.2}=2^n\)
\(\Rightarrow\dfrac{\left(2.2\right)^5.2.2.\left(3.2\right)^5.3.2}{3^5.3.2^5.2}=2^n\)
\(\Rightarrow\dfrac{2^5.2^5.2.2.3^5.2^5.3.2}{3^5.3.2^5.2}=2^n\)
Rút gọn vế trái ta có :
\(2^5.2.2.^5=2^n\)
\(\Rightarrow2^{12}=2^n\)
\(\Rightarrow n=12\) ( Thỏa mãn điều kiện \(n\in N\) )
Vậy n =12
30 tháng 1 2022
=>\(\dfrac{4^5\left(1+1+1+1\right)}{3^5\left(1+1+1\right)}.\dfrac{6^5\left(1+1+1+1+1+1\right)}{2^5\left(1+1\right)}=2^n\)
=>\(\dfrac{4^5.4}{3^5.3}.\dfrac{6^5.6}{2^5.2}=2^n\) =>\(\dfrac{4^6}{3^6}.\dfrac{6^6}{2^6}=2^n\)
=>\(\left(\dfrac{4.6}{3.2}\right)^6=2^n\) =>\(4^6=2^n\) =>\(2^{12}=2^n\) =>n=12.
AH
Akai Haruma
Giáo viên
12 tháng 12 2017
Lời giải:
\(\text{VT}=\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}\)
\(=\frac{4.4^5}{3.3^5}.\frac{6.6^5}{2.2^5}=\frac{4^6.6^6}{3^6.2^6}=\frac{2^{12}.2^6.3^6}{3^6.2^6}=2^{12}\)
Do đó: \(8^{|2x+6|}=2^{12}\Leftrightarrow 2^{3|2x+6|}=2^{12}\)
\(\Leftrightarrow 3|2x+6|=12\Leftrightarrow |2x+6|=4\)
\(\Rightarrow\left[{}\begin{matrix}2x+6=4\\2x+6=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-5\end{matrix}\right.\)
DS
0
Q
12 tháng 12 2017
\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^{\left|2x+6\right|}\)
\(\Leftrightarrow\frac{4.\left(4^5\right)}{3.\left(3^5\right)}.\frac{6.\left(6^5\right)}{2.\left(2^5\right)}=8^{\left|2x+6\right|}\)
\(\Leftrightarrow\frac{4^6.6^6}{3^6.2^3}=8^{\left|2x+6\right|}\)
\(\Leftrightarrow\frac{\left(2^2\right)^6.\left(2.3\right)^6}{3^6.2^3}=8^{\left|2x+6\right|}\)
\(\frac{2^{12}.2^6.3^6}{3^6.2^3}=\frac{2^{18}.3^6}{3^6.2^3}=\frac{2^{15}.1}{1.1}=2^{15}=8^{\left|2x+6\right|}\)
=> 215=(23)|2x+6|
215=23|2x+6|
<=> 3|2x+6|=15
|2x+6|=15:3
|2x+6|=5
\(\Rightarrow\orbr{\begin{cases}2x+6=5\\2x+6=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{-11}{2}\end{cases}}\)
5 tháng 7 2023
1: =1/8*9/4=9/32
2: =8/27*243/32=9/4
3: =(5/4*4/5)^5*(4/5)^2=16/25
4: \(=\left(-\dfrac{5}{6}\cdot\dfrac{6}{5}\right)^2\cdot\left(\dfrac{6}{5}\right)^2=\dfrac{36}{25}\)
5: \(=\left(-\dfrac{4}{3}\right)^3\cdot\left(\dfrac{3}{4}\right)^{10}=\left(-1\right)\left(\dfrac{3}{4}\right)^7=-\left(\dfrac{3}{4}\right)^7\)
6: \(=\left(\dfrac{1}{3}\cdot\dfrac{-9}{2}\right)^4\left(-\dfrac{9}{2}\right)^2=\left(-\dfrac{3}{2}\right)^4\cdot\dfrac{81}{4}=\dfrac{9}{4}\cdot\dfrac{81}{4}=\dfrac{729}{16}\)
8: =(0,2*5)^4*5^2=25
10: =-0,5^5*2^10
=-0,5^5*2^5*2^5
=-32
13: =(0,5*2)^2*2^2=4
\(\dfrac{3}{5}-\dfrac{5}{6}\)
\(=\dfrac{18}{30}-\dfrac{25}{30}\)
\(=-\dfrac{7}{30}\)
7/30