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\(2\cdot3^x+3^{2+x}=891\\\Rightarrow 3^x\cdot2+3^x\cdot3^2=891\\\Rightarrow 3^x\cdot(2+3^2)=891\\\Rightarrow 3^x\cdot(2+9)=891\\\Rightarrow 3^x\cdot 11=891\\\Rightarrow 3^x=891:11\\\Rightarrow 3^x=81\\\Rightarrow 3^x=3^4\\\Rightarrow x=4\)
Vậy $x=4$.
\(2\cdot3^x+3^{2+x}=891\)
=>\(2\cdot3^x+3^x\cdot9=891\)
=>\(3^x=\dfrac{891}{11}=81\)
=>x=4
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5^(2x-3) = 5^2.3 + 2.5^2
5^(2x-3) = 5^2( 3 + 2)
5^(2x-3) = 5^2.5
5^(2x-3) = 5^3
2x - 3 =3
2x = 6
x = 3
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1) (x-3)(x-5) = 0
\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=5\end{cases}}\)
(x+7).35 = 2.35
\(\Rightarrow x+7=2\)
\(\Rightarrow x=2-7=-5\)
Vậy x = -5
2) 1.2 + 2.3 + 3.4 + .... + 99.100
Đặt A = 1.2 + 2.3 + .... + 99.100
3A = 1.2.3 + 2.3.4 + 3.4.3 + .... + 99.100.3
3A = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2)+ .... + 99.100.(101-98)
3A = ( 1.2.3 + 2.3.4 + 3.4.5 +.... + 99.100.101 ) - ( 0.1.2 + 1.2.3 + 2.3.4 + ... + 98.99.100 )
3A = 99.100.101 - 0.1.2
3A = 999900 - 0
3A = 999900
A = 999900 : 3
A = 333300
Vậy A = 333300
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