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`@` `\text {Ans}`
`\downarrow`
`(x - 4)^3 = 64?`
`=> (x - 4)^3 = 4^3`
`=> x - 4 = 4`
`=> x = 4 +4 `
`=> x = 8`
Vậy, `x = 8.`
4^x-5 + 4^x=64
4x : (4.4.4.4.4)+ 4x . 4=64
4x : ( 45+4)=64
4x : 46 = 64
4x : 4096=64
4x =64 . 4096= 262144
4x =49
Vậy x = 9
49 =262144
\(27:x-23:x+4^4:64=216\)
\(\left(27-23\right):x+4^4:4^3=216\)
\(4:x+4=216\)
\(4:x=216-4\)
\(4:x=212\)
\(x=212.4\)
\(x=848\)
Vậy \(x=848\)
643 x 48 x 164
= (26)3 \(\times\) (22)8 \(\times\) (24)4
= 218 \(\times\) 216 \(\times\) 216
= 250
\(4^{x-5}+4^x=64\)
\(\Rightarrow4^{x-5}+4^x=4^3\)
\(\Rightarrow x-5+x=3\)
\(\Rightarrow2x=3+5\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=4\)
\(\Rightarrow2^x+16=64\\ \Rightarrow2^x=48\Rightarrow x\in\varnothing\)
56 . Tính nhanh :
a ) 2 x 31 x 12 + 4 x 6 x 42 + 8 x 27 x 3
b ) 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41
a) 2 x 31 x 12 + 4 x 6 x 42 + 8 x 27 x 3
= 24 x 31 + 24 x 42 + 24 x 27
= 21 x ( 31 + 42 + 27)
= 21 x 100
= 2100
b) 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41
= 36 x ( 28 + 82) + 64 x ( 69 + 41)
= 36 x 110 + 64 x 110
= 110 x ( 36 + 64)
= 110 x 100
= 11000
a) \(\left|x\right|-\frac{7}{6}=\frac{9}{15}\)
=> \(\left|x\right|=\frac{9}{15}+\frac{7}{6}=\frac{53}{30}\)
=> \(\orbr{\begin{cases}x=\frac{53}{30}\\x=-\frac{53}{30}\end{cases}}\)
b) \(\left|x-\frac{4}{3}\right|=\frac{1}{6}\)
=> \(\orbr{\begin{cases}x-\frac{4}{3}=\frac{1}{6}\\x-\frac{4}{3}=-\frac{1}{6}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{7}{6}\end{cases}}\)
c) \(\left|x-\frac{4}{3}\right|-\frac{1}{3}=\frac{1}{2}\)
=> \(\left|x-\frac{4}{3}\right|=\frac{1}{2}+\frac{1}{3}\)
=> \(\left|x-\frac{4}{3}\right|=\frac{5}{6}\)
=> \(\orbr{\begin{cases}x-\frac{4}{3}=\frac{5}{6}\\x-\frac{4}{3}=-\frac{5}{6}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{13}{6}\\x=\frac{1}{2}\end{cases}}\)
d) \(\frac{8}{3}-\left|\frac{7}{9}-x\right|=-\frac{1}{5}\)
=> \(\left|\frac{7}{9}-x\right|=\frac{43}{15}\)
=> \(\orbr{\begin{cases}\frac{7}{9}-x=\frac{43}{15}\\\frac{7}{9}-x=-\frac{43}{15}\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{94}{45}\\x=\frac{164}{45}\end{cases}}\)
e) \(\left|x-\left(\frac{1}{4}\right)^2\right|-\frac{25}{64}=0\)
=> \(\left|x-\frac{1}{16}\right|=\frac{25}{64}\)
=> \(\orbr{\begin{cases}x-\frac{1}{16}=\frac{25}{64}\\x-\frac{1}{16}=-\frac{25}{64}\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{29}{64}\\x=-\frac{21}{64}\end{cases}}\)
f) \(\left(x-\frac{1}{4}\right)^2+\frac{17}{64}=\frac{21}{32}\)
=> \(\left(x-\frac{1}{4}\right)^2=\frac{25}{64}\)
=> \(\left(x-\frac{1}{4}\right)^2=\left(\frac{5}{8}\right)^2\)
=> \(\orbr{\begin{cases}x-\frac{1}{4}=\frac{5}{8}\\x-\frac{1}{4}=-\frac{5}{8}\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{7}{8}\\x=-\frac{3}{8}\end{cases}}\)
=> 4^x=4^3
=>x=3
vậy x=3
Vì 4^x=64 mà 4^3 =64 nên x =3
Đáp số :3