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ND
Nguyễn Đức Trí
VIP
27 tháng 7 2023
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) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)
ND
Nguyễn Đức Trí
VIP
27 tháng 7 2023
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) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)
\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)
\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)
\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)
\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)
\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)
3 tháng 10 2023
a) \(\dfrac{81}{\left(-3\right)^n}=-243\)
\(\dfrac{\left(-3\right)^4}{\left(-3\right)^n}=\left(-3\right)^5\)
\(\left(-3\right)^n=\dfrac{\left(-3\right)^4}{\left(-3\right)^5}=\left(-3\right)^{-1}\)
n = -1
Vậy n = -1
b) \(\dfrac{25}{5^n}=5\)
\(\dfrac{5^2}{5^n}=5^1\)
\(5^n=\dfrac{5^2}{5^1}=5^1\)
n = 1
Vậy n = 1
c) \(\dfrac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)
\(2^{n-1}+4\cdot2^{n-1}\cdot2=9\cdot2^5\)
\(2^{n-1}+8\cdot2^{n-1}=9\cdot2^5\)
\(\left(8+1\right)\cdot2^{n-1}=9\cdot2^5\)
\(9\cdot2^{n-1}=9\cdot2^5\)
\(2^{n-1}=2^5\cdot\dfrac{9}{9}=2^5\)
n - 1 = 5
n = 5 + 1 = 6
Vậy n = 6
KV
3 tháng 10 2023
a) 81/(-3)ⁿ = -243
(-3)ⁿ = 81 : (-243)
(-3)ⁿ = -1/3
n = -1
b) 25/5ⁿ = 5
5ⁿ = 25 : 5
5ⁿ = 5
n = 1
c) 1/2 . 2ⁿ + 4 . 2ⁿ = 9 . 2⁵
2ⁿ . (1/2 + 4) = 9 . 32
2ⁿ . 9/2 = 288
2ⁿ = 288 : 9/2
2ⁿ = 64
2ⁿ = 2⁶
n = 6
7 tháng 7 2017
a) \(\left(\frac{1}{16}\right)^{25}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2^4}\right)^{25}\div\left(\frac{1}{2}\right)^{30}=\left[\left(\frac{1}{2}\right)^4\right]^{25}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2}\right)^{4.25}\div\left(\frac{1}{2}\right)^{30}\)
\(=\left(\frac{1}{2}\right)^{100}\div\left(\frac{1}{2}\right)^{30}=\left(\frac{1}{2}\right)^{100-30}=\left(\frac{1}{2}\right)^{70}\)
b) \(584^{100}\div292^{100}=\left(584-292\right)^{100}=292^{100}\)
c) \(125^4\cdot16^3=\left(5^3\right)^4\cdot\left(2^4\right)^3=5^{3\cdot4}\cdot2^{4\cdot3}=5^{12}\cdot2^{12}=\left(5+2\right)^{12}=7^{12}\)
13 tháng 9 2020
a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=7.\frac{5^8}{5^8}=7\)
b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3.3^8.5^2.5^3}{3.5.5^4.3^8}=\frac{5^5}{5^5}=1\)
c) Đề hơi sai roi bạn oi
d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{61}{50}\)
