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a) \(3\cdot3^4\cdot3^5=3^{10}\)
b) \(7^3:7^2:7=7^{3-2-1}=7^0\)
c) \(\left(x^4\right)^3=x^{12}\)
a) \(\left(x+5\right).6-7=29\)
\(\Rightarrow\left(x+5\right).6=29+7\)
\(\Rightarrow\left(x+5\right).6=36\)
\(\Rightarrow\left(x+5\right)=36:6=6\)
\(\Rightarrow x=6-5=1\)
b) \(5x-3x=12-3.2\)
\(\Rightarrow2x=6\Rightarrow x=6:2=3\)
c) \(\dfrac{1}{4}.3< x< \dfrac{51}{50}.4\)
\(\Rightarrow\dfrac{3}{4}< x< \dfrac{102}{25}\)
a ) 5^n = 125
5^n = 5^3
n = 3
b ) 3^4 . 3^n = 3^7
3^(4 + n ) =3^7
4 + n = 7
n = 7 - 4
n = 3
\(\left(3^7:3^3+4\cdot3^2\right)\cdot3-2^2\cdot2^3\)
\(=\left(3^4+4\cdot9\right)\cdot3-2^5\)
\(=117\cdot3-32\)
\(=351-32=319\)
\(=\left(3^4+4.3^2\right).3-2^2.2^3\\ =\left(81+4.9\right).3-2^2.2^3\\ =117.3-2^5\\ =351-2^5=319\)
Lời giải:
\(\frac{4.3^9+8.(-3)^7}{(-3)^{10}+20.(-3)^7}=\frac{4.3^9-8.3^7}{3^{10}-20.3^7}=\frac{3^7(4.3^2-8)}{3^7(3^3-20)}\\
=\frac{3^7.28}{3^7.7}=\frac{28}{7}=4\)
Lời giải:
\(\frac{4.3^9+8.(-3)^7}{(-3)^{10}+20.(-3)^7}=\frac{4.3^9-8.3^7}{3^{10}-20.3^7}=\frac{3^7(4.3^2-8)}{3^7(3^3-20)}\\ =\frac{3^7.28}{3^7.7}=\frac{28}{7}=4\)
a,-3/5.2/7+-3/7.3/5+-3/7
=-3/7.2/5+(-3/7).3/5+(-3/7)
=-3/7(2/5+3/5+1)
=-3/7.2
=-6/7
\(3^4.3^x=3^7\\ \Rightarrow4+x=7\\ \Rightarrow x=3.\)
\(3^4.3^x=3^7\)
\(81.3^x=2187\)
\(3^x=2187:81\)
\(3^x=27\)
\(\Rightarrow3^2=27\)
\(\Rightarrow x=2\)