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1.
a) 2n : 4 = 16
2n = 16.4
2n = 64
2n = 26
=> n = 6
b) 5n = 625
5n = 54
=> n = 4
c) 2n . 16 = 128
2n = 128 : 16
2n = 8
2n = 23
=> n = 3
d) 3n+3 = 81
3n+3 = 34
=> n + 3 = 4
=> n = 4 - 3
=> n = 1
1.
a) 2n : 4 = 16
2n = 16.4
2n = 64
2n = 26
=> n = 6
b) 5n = 625
5n = 54
=> n = 4
c) 2n . 16 = 128
2n = 128 : 16
2n = 8
2n = 23
=> n = 3
d) 3n+3 = 81
3n+3 = 34
=> n + 3 = 4
=> n = 4 - 3
=> n = 1
2.
a) x3 = 64
x3 = 43
=> x = 4
b) (2x + 1)3 = 27
(2x + 1)3 = 33
2x + 1 = 3
2x = 3 - 1
2x = 2
=> x = 1
c) x3 = x
=> x = {0;1}
d) 25 + 5x = 75.73
25 + 5x = 5764801
5x = 5764801 - 25
5x = 5764776
=> không có số tự nhiên x thoản mãn
a)
\(\Rightarrow3^{-2}.\left(3^3\right)^n=3^n\)
\(\Rightarrow3^{-2}.3^{3n}=3^n\)
\(\Rightarrow3^{3n-2}=3^n\)
\(\Rightarrow3n-2=n\)
\(\Rightarrow n=1\)
b)
\(\Rightarrow3^{4+n-2}=3^7\)
\(\Rightarrow x^{n+2}=3^7\)
\(\Rightarrow n+2=7\)
\(\Rightarrow n=5\)
c)
\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)
\(\Rightarrow2^n.4,5=9.2^5\)
\(\Rightarrow2^n=2.2^5\)
\(\Rightarrow2^n=2^6\)
\(\Rightarrow n=6\)
d)
\(\Rightarrow\left(2^5\right)^{-n}.\left(2^4\right)^n=2048\)
\(\Rightarrow2^{n-5n}=2^{11}\)
\(\Rightarrow-4n=11\)
\(\Rightarrow n=-\frac{4}{11}\)
a)\(\left(\dfrac{1}{2}\right)^n=\dfrac{1}{32}\)
=>\(\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{2}\right)^5\)
=>n=5
b)\(\left(\dfrac{343}{125}\right)=\left(\dfrac{7}{5}\right)^n\)
=>\(\left(\dfrac{7}{5}\right)^3=\left(\dfrac{7}{5}\right)^n\)
=>n=3
c)\(\dfrac{16}{2^n}=2\)
=>2n=\(\dfrac{16}{2}\)
=>2n=8
=>2n=23
=>n=3
d)\(\dfrac{\left(-3\right)^n}{81}=-27\)
=>(-3)n=-27.81
=>(-3)n=-2187
=>(-3)n=(-3)7
=>n=7
e)8n:2n=4
=>(23)n:2n=4
=>23n:2n=4
=>23n-n=4
=>22n=4
=>22n=22
=>2n=2
=>n=1
f)32.3n=35
=>3n=35:32
=>3n=35-2
=>3n=33
=>n=3
g) (22:4).2n=4
=>1.2n=22
=>n=2
h)3-2.34.3n=37
=>\(\left(\dfrac{1}{3}\right)^2\).34.3n=37
=>32.3n=37
=>32+n=37
=>2+n=7
=>n=5
\(\frac{1}{2}.2^n+4.2^n=9.2^5\Rightarrow2^n\left(\frac{1}{2}+4\right)=288\Rightarrow2^n.\frac{9}{2}=288\Rightarrow2^{n-2}.9=288\Rightarrow2^{n-2}=32\)(dấu "=>" số 3 bn sửa thành 2n-1.9=288=>2n-1=32 nha)
=>2n-1=25=>n-1=5=>n=5+1=6
vậy......
~~~~~~~~~~~~~~~
a,
5n + 5n + 2 = 650
=> 5n + 5n.52 = 650
=> 5n(1 + 52) = 650
=> 5n.26 = 650
=> 5n = 25
=> n = 2
a) 5n +5n+2 = 650
5n + 5n.52 = 650
5n.(1+25 ) = 650
5n.26= 650
5n = 25 = 52
=> n = 2
b) 3n+3 +5.3n = 864
3n.33 +5.3n = 864
3n.(33+5) = 864
3n.32 = 864
3n = 27 = 33
=> n = 3
các bài cn lại bn dựa vào mak lm nha!
a: (x-3)2=49
=>x-3=7 hoặc x-3=-7
=>x=10 hoặc x=-4
b: \(\left(x^4\right)^2=\dfrac{x^{12}}{x^5}\)
\(\Leftrightarrow x^8-x^7=0\)
\(\Leftrightarrow x^7\left(x-1\right)=0\)
=>x=0 hoặc x=1
c: \(\Leftrightarrow x^{10}-25x^8=0\)
\(\Leftrightarrow x^8\left(x^2-25\right)=0\)
\(\Leftrightarrow x^8\left(x-5\right)\left(x+5\right)=0\)
hay \(x\in\left\{0;5;-5\right\}\)
a ) ( -2 ) n / 16 = - 32
( -2 ) n = - 512
( -2 ) n = ( - 2 ) 9
=> n = 9
b ) 5 n + 5 n + 2 = 650
5 n ( 1 + 5 2 ) = 650
5 n . 26 = 650
5 n = 25
5 n = 5 2
=> x = 2