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\(3^{x-1}+5.3^{x-1}=162\)
\(\Rightarrow3^{x-1}\left(5+1\right)=162\)
\(\Rightarrow3^{x-1}.6=162\)
\(\Rightarrow3^{x-1}=27\)
\(\Rightarrow3^{x-1}=3^3\)
\(\Rightarrow x-1=3\)
\(\Rightarrow x=4\)
\(3^{x-1}+5.3^{x-1}=162\Rightarrow3^{x-1}\left(1+5\right)=162\Rightarrow3^{x-1}.6=162\)
\(\Rightarrow3^{x-1}=162:6\Rightarrow3^{x-1}=27\Rightarrow x-1=3\Rightarrow x=4\)
\(\frac{2^5.3^7-2^5.3^6}{2^5.3^6}=\frac{2^5.3^6.\left(3-1\right)}{2^5.3^6}=2\)
a) -3/4.x - x = 1
=> x.(-3/4 - 1) = 1
=> x . -7/4 = 1
=> x = 1 : -7/4
=> x = -4/7
b) x5 = (2.x)4
=> x5 = 24 . x4
=> x5 : x4 = 24
=> x5 - 4 = 16
=> x = 16
\(-\frac{3}{4}\cdot x-x=1\)
\(\Rightarrow x\left(-\frac{3}{4}-1\right)=1\)
\(\Rightarrow-\frac{7}{4}x=1\)
\(\Rightarrow x=-\frac{4}{7}\)
\(x^5=\left(2x\right)^4\)
\(\Rightarrow x^5=16x^4\)
\(\Rightarrow x^5-16x^4=0\)
\(\Rightarrow x^4.x-16x^4=0\)
\(\Rightarrow x^4\left(x-16\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^4=0\\x-16=0\end{cases}\Rightarrow}x=16\)
a, Ta có:\(8^{10}=\left(2^3\right)^{10}=2^{30}\)
\(1024^3=\left(2^{10}\right)^3=2^{30}\)
Vậy \(8^{10}=1024^3\)
b, Dựa theo ý a nhưng cơ số là 5\(\Rightarrow25^7>125^3\)
c, Ta có: \(49^{10}\)giữ nguyên
\(625^5=\left(25^2\right)^5=25^{10}\)
50+51+52+53+...+52010+52011
= 1+5+52+53+...+52010+52011
=(1+5)+(52+53)+...+(52010+52011)
= (1+5)+52(1+5)+...+52010(1+5)
= (1+5)(1+52+...+52010)
= 6.(1+52+...+52010) chia hết cho 6
=> đpcm
(2x-2)2 = 16
(2x-2) = 4 vì 4 x 4 = 16
2x = 4 + 2
2x = 6
x = 6 : 2
x = 3
(2x - 2)2 = 16
=> (2x - 2)2 = 42 = (-4)2
=> \(2x-2\in\left\{4;-4\right\}\)
=> \(2x\in\left\{6;-2\right\}\)
=> \(x\in\left\{3;-1\right\}\)
Vậy \(x\in\left\{3;-1\right\}\)
bn cho đề rõ hơn đi
2x - 49 = 5 . 3 mu 2
2x - 49 = 5 .9
2x - 49 = 45
2x = 45 + 49
2x = 94
x = 94 : 2
x= 47
k mk nha