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\(16^x< 128^4\)
=> \(\left[2^4\right]^x< \left[2^7\right]^4\)
=> \(2^{4x}< 2^{28}\)
=> 4x < 28
=> x < 7
Đến đây tìm x được rồi
\(\left[3x^2-5\right]+3^4+6^0=5^3\)
=> \(\left[3x^2-5\right]=5^3-6^0-3^4=43\)
=> \(3x^2-5=43\)
=> \(3x^2=48\)
=> \(x^2=16\)
=> \(x=\pm4\)
\(3x+2x\left[2^3\cdot5-3^2\cdot4\right]+5^2=4^4\)
=> \(3x+2x\left[8\cdot5-9\cdot4\right]+25=256\)
=> \(3x+2x\cdot4+25=256\)
=> \(3x+2x\cdot4=231\)
Đến đây tìm x
1) 2x . 4 = 128
2x = 128 : 4
2x = 32
2x = 25
=> x = 5
2) (2x + 1)3 = 125
(2x + 1)3 = 53
=> 2x + 1 = 5
2x = 5 - 1
2x = 4
x = 2
các bài khác bạn tự làm nha
6x . 6 = 2016
6x = 2016 : 6
6x = 336
=> x \(\in\varnothing\)
42x+3 : 4 = 256
42x+3 = 256 x 4
42x+3 = 1024
42x+3 = 45
2x + 3 = 5
2x = 5 - 3
2x = 2
x = 2 : 2
x = 1
[ x - 2 ]2 = 16
[ x - 2 ]2 = 42
x - 2 = 4
x = 4 + 2
x = 6
[ 2x - 1 ]3 = 27
[ 2x - 1 ]3 = 33
2x - 1 = 3
2x = 3 + 1
2x = 4
x = 4 : 2
x = 2
[ 2x - 1 ]100 = [ 2x - 1 ]100
=> x \(\in N\)
\(1,2x+3x-4x=\left(-2\right)^3\)
<=>\(x=-8\)
\(2,x-2x=4^2+4^0\)
<=>\(-x=16+1\)
<=>\(-x=17\)
<=>\(x=-17\)
\(3,2^3x-3^2x=|12-21|\)
<=>\(-x=9\)
<=>\(x=-9\)
\(4,x-45=2x+54\)
<=>\(x-2x=54+45\)
<=>\(-x=99\)
<=>\(x=-99\)
\(5,5x-12+23=6^7:6^5\)
<=>\(5x+11=6^2\)
<=>\(5x+11=36\)
<=>\(5x=25\)
<=>\(x=5\)
( 2x - 6 ) : 23 = 3
2x - 6 = 3 . 8
2x - 6 = 24
2x = 30
x = 30 : 2 = 15
( 2x - 3 ) : 32 = 9
2x - 3 = 9 . 9
2x - 3 = 81
2x = 81 + 3 = 84
x = 84 : 2 = 42
( 4x - 4 ) : 23 = 6
4x - 4 = 6 . 8
4x - 4 = 48
4x = 48 + 4 = 52
x = 52 : 4 = 13
( 3x - 6 ) : 25 = 3
3x - 6 = 3 . 32
3x - 6 = 96
3x = 96 + 6 = 102
x = 102 : 3 = 34
( 2x - 5 ) : 32 = 5
2x - 5 = 5 . 9
2x - 5 = 45
2x = 45 + 5 = 50
x = 50 : 2 = 25
( 5x - 2 ) : 42 = 3
5x - 2 = 3 . 16
5x - 2 = 48
5x = 48 + 2 = 50
x = 50 : 5 = 10
a: \(\left(x-5\right)^6=\left(x-5\right)^4\)
\(\Leftrightarrow\left(x-5\right)^4\cdot\left[\left(x-5\right)^2-1\right]=0\)
\(\Leftrightarrow\left(x-5\right)^4\cdot\left(x-4\right)\left(x-6\right)=0\)
hay \(x\in\left\{5;4;6\right\}\)
b: \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Leftrightarrow\left(2x-15\right)^3\left(2x-16\right)\left(2x-14\right)=0\)
hay \(x\in\left\{\dfrac{15}{2};8;7\right\}\)
\(\left(2x-2\right)^3=6^4\Leftrightarrow\sqrt[3]{2x-2}=\sqrt[3]{6^4}\\ \Leftrightarrow2x-2=6\sqrt[3]{6}\\ \Rightarrow x=\dfrac{6\sqrt[3]{6}+2}{2}=3\sqrt[3]{6}+1\)
Đs...