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a,\(8< 2^x\le2^9.2^{-5}\)
\(2^3< 2^x\le2^4\)
\(\Rightarrow x=4\)
b, \(27< 81^3.3^x< 243\)
\(3^3< 3^{12-x}< 3^5\)
\(\Rightarrow3< 12-x< 5\)
12-x=4
x=8
c,\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^3.\left(\frac{2}{5}\right)^2\)
\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^5\)
\(\Rightarrow x>5\)
x=6;7;8........
a) \(8< 2^x\le2^9.2^{-5}\)
\(\Leftrightarrow2^3< x\le2^{9-5}\)
\(\Leftrightarrow2^3< 2^x\le2^4\)
\(\Leftrightarrow3< x\le4\Leftrightarrow x=4\)
b) \(27< 81^3:3^x< 243\)
\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)
\(\Leftrightarrow2< 12-x< 5\)
\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)
1.
a) \(x\in\left\{4;5;6;7;8;9;10;11;12;13\right\}\)
b) x=0
d) \(x=\frac{-1}{35}\) hoặc \(x=\frac{-13}{35}\)
e) \(x=\frac{2}{3}\)
Bài 3: Tìm x:
a. \(\left(2x-1\right)^4=81\)
\(\Rightarrow\left(2x-1\right)^4=3^4\)
=> 2x - 1 = 3
=> 2x = 4
=> x = 2
b. \(\left(x-2\right)^2=1\)
\(\Rightarrow\) \(\left(x-2\right)^2=1^2\)
=> x - 2 = 1
=> x = 3
c. \(x^{2000}=x\)
=> x = 1
d. \(\left(4x-3\right)^3=-125\)
\(\Rightarrow\left(4x-3\right)^3=\left(-5\right)^3\)
=> 4x - 3 = -5
=> 4x = -2
=> x = \(\dfrac{-1}{2}\)
a) 32 < 2^n < 128
hay 2^5 < 2^n < 2^7
=> 5 < n < 7
=> n = 6
b) 2.16 \(\ge\)2^n > 4
hay 2^5 \(\ge\)2^n > 2^2
=> 5 \(\ge\)n > 2
=> n \(\in\left\{5;4;3\right\}\)
c) 9.27 \(\le\)3^n \(\le\) 243
hay 3^5 \(\le\)3^n \(\le\) 3^5
=> 5 \(\le\) n \(\le\) 5
=> n = 5
a,32<2^n<128
n sẽ bằng 6 vì khi 2^6=64>32 và 2^6=64 <128 (thỏa mãn điều kiện)
Vậy :n=6
lm tương tự
a) \(\left(2^2:4\right).2^n=2=32\)
\(\Leftrightarrow\left(2^2:2^2\right).2^n=2^5\)
\(\Leftrightarrow2^{2-2}.2^n=2^5\)
\(\Leftrightarrow2^0.2^n=2^5\)
\(\Leftrightarrow1.2^n=2^5\)
\(\Leftrightarrow2^n=2^5\)
\(\Leftrightarrow n=5\)
Vậy n=5
b) \(27< 3^n< 243\)
\(\Leftrightarrow3^3< 3^n< 3^5\)
\(\Leftrightarrow3< n< 5\)
\(\Rightarrow n=4\)
Vậy n=4
a. \(\left(2^2:4\right).2^n=32\)
\(\Rightarrow\left(4:4\right).2^n=32\)
\(\Rightarrow2.2^n=32\)
\(\Rightarrow2^n=32:1=32=2^5\)
\(\Rightarrow n=5\)
Vậy................
b. \(27< 3^n< 243\)
\(\Leftrightarrow3^3< 3^n< 3^5\)
\(\Rightarrow3< n< 5\)
\(\Rightarrow n=4\)
c. đề bài có j đó sai sai