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mình lớp 6 thử làm thôi nha
a) 2225 = 25.45 = ( 245 ) 5
3150 = 35.30 = ( 330 ) 5
ta thấy hai lũy thừa đã cùng số mũ nên ta so sánh cơ số
245 = 29.5 = ( 29 ) 5 = 5125
330 = 36.5 = ( 36 ) 5 = 7295
Vì 512 < 729 nên 2225 < 3150
a/\(2^{225}=\left(2^3\right)^{75}=8^{75}\)
\(3^{150}=\left(3^2\right)^{75}=9^{75}\)
\(8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)
b/ \(2^{24}=\left(2^3\right)^8=8^8\)
\(3^{16}=\left(3^2\right)^8=9^8\)
\(8^8< 9^8\Rightarrow2^{24}< 3^{16}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)
\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)
\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)
\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)
\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)
\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 13 : So sánh
2225 và 3150
Ta có :
2225 = ( 23 )75 = 875
3150 = ( 32 )75 = 975
Vì 875 < 975 ( 8 < 9 )
Nên 2225 < 3150
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
\(2^{90}\) và \(5^{36}.\)
Ta có:
\(2^{90}=\left(2^5\right)^{18}=32^{18}.\)
\(5^{36}=\left(5^2\right)^{18}=25^{18}.\)
Vì \(32>25\) nên \(32^{18}>25^{18}\)
\(\Rightarrow2^{90}>5^{36}.\)
Bài 3:
Ta có: \(\frac{a}{b}=\frac{c}{d}.\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{c^2}{d^2}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a^2+c^2}{b^2+d^2}\) (1)
\(\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a^2-c^2}{b^2-d^2}\) (2)
Từ (1) và (2) \(\Rightarrow\frac{a^2+c^2}{b^2+d^2}=\frac{a^2-c^2}{b^2-d^2}.\)
\(\Rightarrow\frac{a^2+c^2}{a^2-c^2}=\frac{b^2+d^2}{b^2-d^2}\left(đpcm\right).\)
Chúc bạn học tốt!
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\(A=1+2+2^2+...+2^{2017}\)
\(\Rightarrow A=\dfrac{2^{2017+1}-1}{2-1}\)
\(\Rightarrow A=2^{2018}-1\)
mà \(B=2^{2018}\)
\(\Rightarrow A-B=2^{2018}-1-2^{2018}\)
\(\Rightarrow A-B=-1\)
\(2A=2+2^2+2^3+...+2^{2018}\)
\(\Rightarrow A=2A-A=2^{2018}-1\)
\(\Rightarrow A-B=2^{2018}-1-2^{2018}=-1\)