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a: \(\Leftrightarrow2^5\ge2^n>2^2\)
=>2<n<=5
hay \(n\in\left\{3;4;5\right\}\)
b: \(\Leftrightarrow3^2\cdot3^3\le3^n\le3^5\)
=>5<=n<=5
=>n=5
a) \(9.3^3.\frac{1}{81}.3^2=3^2.3^3.\frac{1}{3^4}.3^2=3^7.\frac{1}{3^4}=3^3\)
b) \(4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:2^3:\frac{1}{16}=2^7:2^3.16=2^4.2^4=2^8\)
c) \(3^2.2^5.\left(\frac{2}{3}\right)^2=3^2.2^5.\frac{2^2}{3^2}=2^5.2^2=2^7\)
d) \(\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^3.\left(3^2\right)^2=\frac{1^3}{3^3}.3^4=1^3.3=3^1\)
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) \(\left(\frac{1}{3}\right)^{^2}.\frac{1}{3}.9^2=3=3^1\)(viết dưới dạng lũy thừa)
B)\(8< 2^n< 2.16\)
\(2^3< 2^n< 2.2^4\)
\(2^3< 2^n< 2^5\)
\(\Rightarrow3< n< 5\)
mà n là số tự nhiên => n = 4
C) |-x| = 1 => |x| = 1 => x = -1 hoặc x = 1.
|2x| = 6.7 + (-3,3) - 0.4 = 42 - 3,3 - 0 = 42 - 3,3 = 38,7
=> 2x = 38,7 hoặc 2x = -38,7
=> x = 19,35 hoặc x = -19,35
\(8^n:2^n=4\)
\(\Leftrightarrow\left(2^3\right)^n:2^n=2^2\)
\(\Leftrightarrow2^{3n}:2^n=2^2\)
\(\Leftrightarrow3n-n=2\)
\(\Leftrightarrow2n=2\)
\(\Leftrightarrow n=1\)
\(\frac{x^7}{81}=27\Rightarrow x^7=27.81\Rightarrow x^7=3^3.3^4\Rightarrow x^7=3^7\Rightarrow x=3\)
\(\frac{x^8}{9}=729\Rightarrow x^8=729.9\Rightarrow x^8=3^6.3^2\Rightarrow x^8=3^8\Rightarrow x=3\)
a: Đặt f(x)=0
=>3/4x=1/8
=>x=1/8:3/4=1/8x4/3=4/24=1/6
b: Đặt H(x)=0
=>-5x+30=0
=>x=6
c: Đặt G(x)=0
=>(x-3)(x-4)=0
=>x=3 hoặc x=4
d: Đặt K(x)=0
=>(x-9)(x+9)=0
=>x=9 hoặc x=-9
e: Đặt M(x)=0
=>(x+8)(x-1)=0
=>x=-8 hoặc x=1
a,\(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2\)
\(=\left(\dfrac{13}{14}\right)^2\)
\(=\dfrac{169}{196}\)
b,\(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=\left(\dfrac{-1}{12}\right)^2\)
\(=\dfrac{1}{144}\)
c,\(\dfrac{5^4.20^4}{25^5.4^5}\)
\(=\dfrac{100^4}{100^5}\)
\(=\dfrac{1}{100}\)
d,\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4\)
\(=\left(\dfrac{-10}{3}\right)^4.\left(\dfrac{-6}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)
\(=\left(\dfrac{\left(-10\right)}{3}.\dfrac{\left(-6\right)}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)
\(=4^4.\left(\dfrac{-10}{3}\right)\)
\(=256.\left(\dfrac{-10}{3}\right)\)
\(=\dfrac{-2560}{3}\)
a) \(\frac{16}{2^n}=2\)
=> 2.2n = 16
=> 21+n = 24
=> 1 + n = 4
=> n = 4 - 1
=> n = 3
Vậy n = 3
b) \(\frac{\left(-3\right)^n}{81}=-27\)
=> (-3)n = -27.81
=> (-3)n = -33.34
=> (-3)n = (-3)7
=> n = 7
Vậy n = 7
c) 8n : 2n = 4
=> (8 : 2)n = 4
=> 4n = 41
=> n = 1
Vậy n = 1