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\(\dfrac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\dfrac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^n\)
<=>\(\dfrac{4.4^5}{3.3^5}\cdot\dfrac{6.6^5}{2.2^5}=2^n\)
<=>\(\dfrac{4^6.6^6}{3^6.2^6}\)=2n
<=>\(\dfrac{\left(4.6\right)^6}{\left(3.2\right)^6}=2^n\)
<=>46=2n
<=>(22)6=2n
<=>2n=212
<=>n=12
Câu hỏi của Lê Khánh Nhi - Toán lớp 7 - Học toán với OnlineMath sửa n thành x cho sửa cho nó thành lũy thừa luôn
Tìm x,biết
\(\dfrac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\dfrac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)
\(\dfrac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\dfrac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}\)
\(=\dfrac{4.4^5.6.6^5}{3.3^5.2.2^5}\)
\(=\dfrac{4^6.6^6}{3^6.2^6}\)
\(=\dfrac{2^6.2^6.2^6.3^6}{3^6.2^6}\)
\(=2^{12}=2^{3^4}=8^4=8^x\)
Vậy x = 4
45+45+45+4535+35+35.65+65+65+65+65+6525+2545+45+45+4535+35+35.65+65+65+65+65+6525+25
=4.45.6.653.35.2.25=4.45.6.653.35.2.25
=46.6636.26=46.6636.26
=26.26.26.3636.26=26.26.26.3636.26
=212=234=84=8x=212=234=84=8x
Vậy x = 4
a) Ta có:
+) a/2=b/3
=>a=2b/3
+) b/5=c/4
=>c=4b/5
Lại có:
a-b+c=49
=> 2b/3 -b + 4b/5 =49
=> 7b/15==49
=> b= 105
Khi đó:
+) a=2b/3=2.105/3=70
+)c=4b/5=4.105/5=84
Vậy a=70; b=105; c=84...
chúc bạn học tốt
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: \(8^{|2x+6|}=2^{12}\Leftrightarrow 2^{3|2x+6|}=2^{12}\)
\(\Leftrightarrow 3|2x+6|=12\Leftrightarrow |2x+6|=4\)
\(\Rightarrow\left[{}\begin{matrix}2x+6=4\\2x+6=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-5\end{matrix}\right.\)
\(\left(\dfrac{3^2.3^4}{6^5.9}\right)^4:\left(\dfrac{2^4}{64}\right)^{12}\)
=\(\left(\dfrac{3^4}{6^5}\right)^4:\left(\dfrac{16}{64}\right)^{12}\)
=\(\left(\dfrac{1}{96}\right)^4:\left(\dfrac{1}{4}\right)^{12}\)
=\(\dfrac{1}{96^4}:\dfrac{1}{4^{12}}\)
=\(\dfrac{4^{12}}{96^4}\)
\(=\frac{4\cdot4^5}{3\cdot3^5}\cdot\frac{6\cdot6^5}{2\cdot2^5}=\frac{4^6}{3^6}\cdot\frac{6^6}{2^6}=\frac{2^{12}\cdot2^6\cdot3^6}{3^6\cdot2^6}=2^{12}=2^n\Rightarrow n=12\)
câu 5 :vì đồ thị của hàm số y =ax (a khác 0) là 1 đường thẵng đi qua góc toạ độ nên 3 điểm o,m,m là 1 đường thẳng ,k nha
\(\dfrac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\dfrac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^n\)
\(\Rightarrow\dfrac{4^5.4}{3^5.3}.\dfrac{6^5.6}{2^5.2}=2^n\)
\(\Rightarrow\dfrac{4^5.4.6^5.6}{3^5.3.2^5.2}=2^n\)
\(\Rightarrow\dfrac{\left(2.2\right)^5.2.2.\left(3.2\right)^5.3.2}{3^5.3.2^5.2}=2^n\)
\(\Rightarrow\dfrac{2^5.2^5.2.2.3^5.2^5.3.2}{3^5.3.2^5.2}=2^n\)
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