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Bài 6 :
a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)
b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)
c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)
d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)
Bài 7 :
a) \(3^x+3^{x+2}=9^{17}+27^{12}\)
\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)
\(\Rightarrow10.3^x=3^{34}+3^{36}\)
\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)
\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)
b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)
\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)
\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)
c) Bài C bạn xem lại đề
d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)
\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)
\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)
\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)
\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)
\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)
a,Ta có \(16<2^n\le2^3.32\)
<=>\(2^4<2^n\le2^3,2^5\)
<=> \(2^4<2^n\le2^8\)
<=> \(4 < n \le 8\)
=> \(n \in{5,6,7,8}\)
b, \(25<5^n<625\)
<=>\(5^2 < 5^n<5^4\)
<=> 2<n<4
=> n=3
Ta có:\(25< 5^n< 625\)
\(\Leftrightarrow5^2< 5^n< 5^4\)
\(\Leftrightarrow2< x< 4\)
\(\Leftrightarrow x=3\)
Vậy \(x=3\)
6, Lập các TLT từ 4 trong 5 số sau:
1; 5; 25; 125; 625
=> \(\dfrac{25}{5}=\dfrac{625}{125},\dfrac{25}{625}=\dfrac{5}{125},\dfrac{625}{25}=\dfrac{125}{5},\dfrac{625}{125}=\dfrac{25}{5}\)
Bài 2:
a) Ta có: \(f\left(2\right)-f\left(-1\right)=7\)
\(\Leftrightarrow2\left(m-1\right)-\left(-1\right)\cdot\left(m-1\right)=7\)
\(\Leftrightarrow2m-2+m-1=7\)
\(\Leftrightarrow3m-3=7\)
\(\Leftrightarrow3m=10\)
hay \(m=\dfrac{10}{3}\)
Ta có: 3.81 = 9.27
=> Lập được các tỉ lệ thức sau:
+) \(\frac{3}{9}=\frac{27}{81}\)
+) \(\frac{3}{27}=\frac{9}{81}\)
+) \(\frac{81}{9}=\frac{27}{3}\)
+) \(\frac{81}{27}=\frac{9}{3}\)
b) Ta có: 5.25 = 125.1
=> Lập được các tỉ lệ thức sau:
+) \(\frac{5}{125}=\frac{1}{25}\)
+) \(\frac{5}{1}=\frac{125}{25}\)
+) \(\frac{25}{125}=\frac{1}{5}\)
+) \(\frac{25}{1}=\frac{125}{5}\)
Ta có: 5.125 = 625.1
=> Lập được các tỉ lệ thức sau:
+) \(\frac{5}{625}=\frac{1}{125}\)
+) \(\frac{5}{1}=\frac{625}{125}\)
+) \(\frac{125}{625}=\frac{1}{5}\)
+) \(\frac{125}{1}=\frac{625}{5}\)
Ta có: 625.5 = 125.25
+) \(\frac{625}{125}=\frac{25}{5}\)
+) \(\frac{625}{25}=\frac{125}{5}\)
+) \(\frac{5}{125}=\frac{25}{625}\)
+) \(\frac{5}{25}=\frac{125}{625}\)
P/s: Ko chắc !
C = 25.{2 + 3.[5. (625.25]}
C = 25.{2 + 3.[5.15625]}
C = 25.{2 + 3.78125}
C = 25.{2 + 234375}
C = 25.234377
C = 5859425