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1. So sánh
a) \(25^{50}\) và \(2^{300}\)
\(25^{50}=25^{1.50}=\left(25^1\right)^{50}=25^{50}\)
\(2^{300}=2^{6.50}=\left(2^6\right)^{50}=64^{50}\)
Vì \(25< 64\) nên \(25^{50}< 64^{50}\)
Vậy \(25^{50}< 2^{300}\)
b) \(625^{15}\) và \(12^{45}\)
\(625^{15}=625^{1.15}=\left(625^1\right)^{15}=625^{15}\)
\(12^{45}=12^{3.15}=\left(12^3\right)^{15}=1728^{15}\)
Vì \(625< 1728\) nên \(625^{15}< 1728^{15}\)
Vậy \(625^{15}< 12^{45}\)
1.So sánh
a)\(25^{50}\) và \(2^{300}\)
Ta có : \(2^{300}=\left(2^6\right)^{50}=64^{50}\)
Vì \(25^{50}< 64^{50}\) nên \(25^{50}< 2^{300}\)
b)\(625^{15}\) và \(12^{45}\)
Ta có : \(12^{45}=\left(12^3\right)^{15}=1728^{15}\)
Vì \(625^{15}< 1728^{15}\) nên \(625^{15}< 12^{45}\)
a)\(\left(5x+1\right)^2=\frac{36}{49}\\ \left(5x+1\right)^2=\left(\frac{6}{7}\right)^2\\ \Rightarrow\left[{}\begin{matrix}5x+1=\frac{6}{7}\\5x+1=\frac{-6}{7}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{-1}{35}\\x=\frac{-13}{35}\end{matrix}\right.\)
vậy...
2.
a) \(\left(5x+1\right)^2=\frac{36}{49}\)
⇒ \(5x+1=\pm\frac{6}{7}\)
⇒ \(\left[{}\begin{matrix}5x+1=\frac{6}{7}\\5x+1=-\frac{6}{7}\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}5x=\frac{6}{7}-1=-\frac{1}{7}\\5x=\left(-\frac{6}{7}\right)-1=-\frac{13}{7}\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=\left(-\frac{1}{7}\right):5\\x=\left(-\frac{13}{7}\right):5\end{matrix}\right.\)
⇒ \(\left[{}\begin{matrix}x=-\frac{1}{35}\\x=-\frac{13}{35}\end{matrix}\right.\)
Vậy \(x\in\left\{-\frac{1}{35};-\frac{13}{35}\right\}.\)
Chúc bạn học tốt!
\(3:\frac{9}{4}=\frac{3}{4}:6x\)
\(\Leftrightarrow\frac{3}{4}:6x=\frac{12}{9}\)
\(\Leftrightarrow\frac{3}{4}:6x=\frac{4}{3}\)
\(\Leftrightarrow6x=\frac{3}{4}:\frac{4}{3}\)
\(\Leftrightarrow6x=\frac{9}{16}\)
\(\Leftrightarrow x=\frac{3}{32}\)
a) \(5^n.25=125^2\)
\(\Rightarrow5^n.5^2=\left(5^3\right)^2\)
\(\Rightarrow5^n.5^2=5^6\)
\(\Rightarrow5^n=5^6:5^2\)
\(\Rightarrow5^n=5^4\)
\(\Rightarrow n=4\)
Vậy \(n=4.\)
b) \(3^n.9^2=27^3\)
\(\Rightarrow3^n.\left(3^2\right)^2=\left(3^3\right)^3\)
\(\Rightarrow3^n.3^4=3^9\)
\(\Rightarrow3^n=3^9:3^4\)
\(\Rightarrow3^n=3^5\)
\(\Rightarrow n=5\)
Vậy \(n=5.\)
c) \(2^4.4^n=8^6\)
\(\Rightarrow\left(2^2\right)^2.4^n=2^{18}\)
\(\Rightarrow4^2.4^n=\left(2^2\right)^9\)
\(\Rightarrow4^2.4^n=4^9\)
\(\Rightarrow4^n=4^9:4^2\)
\(\Rightarrow4^n=4^7\)
\(\Rightarrow n=7\)
Vậy \(n=7.\)
Chúc bạn học tốt!
1.
\(x=\dfrac{3}{17}\Rightarrow\left|x\right|=\left|\dfrac{3}{17}\right|=\dfrac{3}{17}\)
\(x=-\dfrac{13}{161}\Rightarrow\left|x\right|=\left|-\dfrac{13}{161}\right|=\dfrac{13}{161}\)
\(x=-15,08\Rightarrow\left|x\right|=\left|-15,08\right|=15,08\)
2.(Bài này mình lấy máy tính bấm luôn á! Nếu GV yêu cầu bạn quy đồng thì bạn tự quy đồng nha!
)
\(\dfrac{-6}{25}+\left|-\dfrac{4}{5}\right|-\dfrac{2}{25}\\ =\dfrac{-6}{25}+\dfrac{4}{5}-\dfrac{2}{25}\\ =\dfrac{12}{25}\)
\(\dfrac{5}{9}-\left|-\dfrac{3}{5}\right|+\dfrac{4}{9}+\dfrac{8}{5}\\ =\dfrac{5}{9}-\dfrac{3}{5}+\dfrac{4}{9}+\dfrac{8}{5}\\ =\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\left(-\dfrac{3}{5}+\dfrac{8}{5}\right)\\ =1+1\\ =2\)
Chúc bạn học giỏi!
a ) \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)và \(x+z=18\)
Áp dụng t/c dãy tỏ số bằng nhau ta có :
\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{x+z}{2+4}=\frac{18}{6}=3\)
\(\Rightarrow\hept{\begin{cases}\frac{x}{2}=3\\\frac{y}{3}=3\\\frac{z}{4}=3\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=6\\y=9\\z=12\end{cases}}\)
b ) \(\frac{x}{5}=\frac{y}{-6}=\frac{z}{7}\) và \(y-x=39\)
Áp dụng t/c dãy tỉ số bằng nhau ta có :
\(\frac{x}{5}=\frac{y}{-6}=\frac{z}{7}=\frac{y-x}{-6-5}=\frac{39}{-11}\)
\(\Rightarrow\hept{\begin{cases}\frac{x}{5}=\frac{39}{-11}\\\frac{y}{-6}=\frac{39}{-11}\\\frac{z}{7}=\frac{39}{-11}\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\frac{195}{11}\\y=-\frac{234}{11}\\z=\frac{273}{11}\end{cases}}\)
Bài 1: a) (2x+1)2 = 25
(2x+1)2 = 52
=> 2x + 1 = 5 hoặc 2x+1 = -5
=> x=2 hoặc x=-3
b) 2x+2 - 2x = 96
<=> 2x . 22 - 2x = 96
<=> 2x(4-1) =96
<=>2x = 96 :3 = 32 = 25
<=> x = 5
c) (x-1)3 = 125
<=> (x-1)3 = 53
<=> x-1=5
<=>x= 5 +1 = 6
a)
\(3:\left(\dfrac{9}{4}\right)=\dfrac{3}{4}:\left(6.x\right)\\ \Rightarrow3.6.x=\dfrac{3}{4}.\dfrac{9}{4}\\ x=\dfrac{3}{4}.\dfrac{9}{4}.\dfrac{1}{3}.\dfrac{1}{6}\\ x=\dfrac{3}{4.4.2}\\ x=\dfrac{3}{32}\)
b)
\(4,5:0,3=\left(5.0,09\right):\left(0,01.x\right)\\ 0,01.x.4,5=5.0,09.0,3\\ x=5.\dfrac{9}{100}.\dfrac{3}{10}.100.\dfrac{10}{45}\\ x=3\)
d)
\(\left(\dfrac{1}{9}.x\right)=\dfrac{7}{4}:\dfrac{2}{25}\\ \left(\dfrac{1}{9}.x\right)=\dfrac{7}{4}.\dfrac{25}{2}\\ x:\dfrac{7}{4}=\dfrac{25}{2}:\dfrac{1}{9}\\ x=\dfrac{25}{2}.9.\dfrac{7}{4}\\ x=\dfrac{1575}{8}\\ x=196\dfrac{7}{8}\)
e)
\(\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}\\ -x.x=-2.\dfrac{8}{25}\\ -x^2=-\dfrac{16}{25}=-\dfrac{4^2}{5^2}\\ -x^2=-\left(\dfrac{4}{5}\right)^2\\ \Rightarrow x=\dfrac{4}{5}\)
Chúc bạn học tốt