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a) x=3
b) x=1
c) x=1 hoặc -5
d) x=2
e) x=2
g) x=2
h) x=1 hoặc x=0 hoặc x=-1
i) x=-1 hoặc x=0
\(a.4^x=64\)
\(4^x=4^3\)
\(\Rightarrow x=3\)
\(b,3^{x\times4}=81\)
\(3^{x\times4}=3^4\)
\(x\times4=4\)
\(\Rightarrow x=1\)
\(c,\left(2+x\right)^4=81\)
\(\left(2+x\right)^4=3^4\)
\(2+x=3\)
\(x=3-2\)
\(x=1\)
\(d,5^{x\times5}=125\)
\(5^{x\times5}=5^3\)
\(x\times5=3\)
\(x=3:5\)
\(x=\frac{3}{5}\)
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1. a) 4.415.8.25.125
= (4.25). (8.125).415
= 100.1000.415
= 100000.415
= 41500000
b) 2.31.12+4.42.6+8.27.3
= (2.31.12)+(4.42.6)+(8.27.3)
= (2.12).31+(4.6).42+(8.3).27
= 24.31+24.42+24.27
= 24 (31+42+27)
= 24.100
= 2400
1/ a) \(2.3.12.12.3=2.3.2^2.3.2^2.3.3=2^5.3^4\)
b) \(3.5.27.125=3.5.3^3.5^3=3^4.5^4=\left(3.5\right)^4\)
2/ a) \(\left(27^3\right)^4=27^{3.4}=27^{12}\)
Vậy \(\left(27^3\right)^4=27^{12}\)
b) \(5^{36}=\left(5^6\right)^6\) và \(11^{24}=\left(11^4\right)^6\)
Do đó \(5^6=15625\) và \(11^4=14641\)
Vì 15625>14641 nên\(\left(5^6\right)^6>\left(11^4\right)^6hay5^{36}>11^{24}.\)
3/ a) \(x^3=125=>x=5\)
b) \(\left(3x-14\right)^3=2^5.5^2+200\)
\(\left(3x-14\right)^3=1000\)
\(3x-14=10^3\)
\(3x=10^3+14\)
\(3x=1014\)
\(x=\frac{1014}{3}=338\)
c) \(\left(2x-1\right)^4=81\)
\(\left(2x-1\right)^4=3^4\)
\(2x-1=3\)
\(2x=3+1\)
\(x=\frac{4}{2}=2\)
d) \(5x+3^4=2^2.7^2\)
\(5x+3^4=\left(2.7\right)^2=14^2\)
\(5x+81=196\)
\(5x=196-81\)
\(5x=115\)
\(x=\frac{115}{5}=23\)
e) \(4^x=1024=>x=5\).
1a.4,9,16,25,36,49,64,91,110,121,144,169,400,900,1600
b. 8,27,64,125,1000
C1111^2=1234321
2. x=6 ,x=3,x=0, x k thuộc n, x k thuộc n
a: \(2^x=2^3\)
nên x=3
c: \(11^x=1331\)
nên x=3
d: \(2^x+4=12\)
nên \(2^x=8\)
hay x=3