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a) \(2^x=16=2^4\Rightarrow x=4\)
b) \(x^3=27=3^3\Rightarrow x=3\)
c) \(x^{50}=x\Rightarrow x\left(x^{49}-1\right)=0\Rightarrow x=0\) hay \(x=1\)
d) \(\left(x-2\right)^2=16=4^2\Rightarrow x-2=4\) hay \(x-2=-4\)
\(\Rightarrow x=6\) hay \(x=-2\)
a) \(2^{300}=2^{3.100}=8^{100}\)
\(3^{200}=3^{2.100}=9^{100}\)
vì \(8^{100}< 9^{100}\)
\(\Rightarrow2^{300}< 3^{200}\)
b) \(3^{500}=3^{5.100}=243^{100}\)
\(7^{300}=7^{3.100}=343^{100}\)
vì \(243^{100}< 343^{100}\)
\(\Rightarrow3^{500}< 7^{300}\)
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(x-32):16=48
=> x-32=48.16
=> x-32=768
=> x=768+32
=> x=800
x-32:16=48
=> x-2=48
=> x=48+2
=> x=50
( x - 32 ) : 16 = 48
x - 32 = 48 . 16
x - 32 = 768
x = 768 + 32= 800
x - 32 : 16= 48
x - 2 = 48
x = 48 + 2= 50
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a: \(x\in\left\{4;8;16\right\}\)
b: \(x\in\left\{26;39;52;65;78\right\}\)
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a)\(\dfrac{4}{x}=\dfrac{x}{16}\)
<=>\(x^2=4.16=64\)
<=>\(x=\pm8\)
<=>x=-8(vì x<0)
b)\(\dfrac{x}{-24}=\dfrac{-6}{x}\)
<=>\(x^2=\left(-24\right)\left(-6\right)=144\)
<=>\(x=\pm12\)
<=>x=12(Vì x>0)
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Ta có \(\frac{x}{5}=\frac{y}{3}\) và \(x+y=16\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{x}{5}=\frac{y}{3}=\frac{x+y}{5+3}=\frac{16}{8}=2\)
\(\Rightarrow x=2.5=10\) và \(y=2.3=6\)
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Ta có: \(48⋮x-2\)
\(\Leftrightarrow x-2\in\left\{16;24\right\}\)
hay \(x\in\left\{18;26\right\}\)
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Ta có: \(48⋮x-2\)
\(\Leftrightarrow x-2\in\left\{1;2;3;4;6;8;12;16;24;48\right\}\)
mà 16<x<48
nên \(x\in\left\{18;26\right\}\)