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a, 4^x +4^x .4 =20
4^x(1+4) =20
4^x .5 =20
4^x =20:5
4^x = 4
x = 1
b,7^x .7^2=7^90
7^x = 7^90:7^2
7^x =7^88
x = 88
c, 5^x +5^x.5 = 750
5^x(1+5) =750
5^x . 6 =750
5^x = 750:6
5^x =125
5^x = 5^3
x =3
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a)5x+1=125
=>5x+1=53
=>x+1=3
=>x=2
vậy x=2
b)42x+1=64
=>42x+1=43
=>2x+1=3
=>x=1
vậy x =1
e)=>43x+2017=42020-3
=>3x+2017=2017
=>x=0
vậy x=0
f)=>2x+2x x 23=144
=>2x x (1+23)=144
=>2x x 9=144
=>2x=16
=>2x=24
=>x=4
vậy x=4
2a/ 2x - 3 = 16 => 2x - 3 = 24 => x - 3 = 4 => x = 7
b/ {x2 - [82 - (52 - 8.3)3 - 7.9]3 - 4.12}3 = 1
=> x2 - [82 - (52 - 8.3)3 - 7.9]3 - 4.12 = 1
=> x2 - [64 - (25 - 24)3 - 63]3 - 48 = 1
=> x2 - (64 - 1 - 63)3 = 1 + 48
=> x2 - 0 = 49
=> x2 = 49
=> x = 7
\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)
<=>\(2^x+2^x.2+2^x.4+2^x.8=480\)
<=>\(2^x\left(1+2+4+8\right)=480\)
<=>\(2^x.15=480\)
<=>\(2^x=32\)
=>\(x=5\)
a) \(S=4^0+4^1+4^2+...+4^{35}\)
\(S=\left(4^0+4^1+4^2\right)+...+\left(4^{33}+4^{34}+4^{35}\right)\)
\(S=21+...+4^{33}\cdot\left(1+4+4^2\right)\)
\(S=21+...+4^{33}\cdot21\)
\(S=21\cdot\left(1+...+4^{33}\right)⋮21\left(đpcm\right)\)
a) 3x = 33.35 = 38
=> x = 8
b) 2x.2 = 222
2x+1 = 22
=> x + 1 = 22
x = 21
c) (7x-11)3 = 25.52 + 200 = 800 + 200 = 1 000 = 103
=> 7x -11 = 10
7x = 21
x = 3
d) 6x = 362 = (62)2 = 64
=> x = 4
e) 64.4x = 49
4x = 49/64
f) (21-1)3 = 203 ( xem lại đề)
h) 64.4x.2 = 45
4x.128 = 45
4x = 45/128
a) 412 - ( 324 - x ) = 543
324 - x = 412 - 543
324 - x = -131
x = 324 - (-131 )
x = 455
a) 412-(324-x)=543
324-x=412-543
324-x=-131
x=324+131
x=455
b) 3.(x+41)=153
x+41=51
x=51-41=10
c) 276-5(x+2)=56
5(x+2)=220
x+2=44
x=44-2=42
d) 10+2x=415:412
10+2x=43
10+2x=64
2x=64-10=54
x=54:2=27
e) 5x-206=24.4
5x-206=24.22
5x-206=26
5x-206=64
5x=270
x=270:5=54
5 . 2^x - 1 = 40
2^x - 1 = 40 : 5
2^x - 1 = 8
2^x-1 = 2^3
=> x - 1 = 3
x = 3 + 1
x = 4
4^x+1 = 64
4^x+1 = 4^3
=> x + 1 = 3
x = 3 - 1
x = 2
5 . 2x-1 = 40
2x-1 = 40 : 5
2x-1 = 8
2x-1 = 23
x - 1 = 3
x = 3 + 1
x = 4
4x+1 = 64
4x+1 = 43
x + 1 = 3
x = 3 - 1
x = 2