9^x=5.9^7+4.9^7
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a: \(=\dfrac{4\cdot11\cdot3}{4\cdot9}\cdot\dfrac{1}{121}=\dfrac{11}{121}\cdot\dfrac{1}{3}=\dfrac{1}{33}\)
b: \(=\dfrac{7}{9}\left(\dfrac{3}{4}+\dfrac{1}{4}\right)=\dfrac{7}{9}\)
c: \(=\dfrac{-6}{7}-\dfrac{1}{7}+\dfrac{2}{11}+\dfrac{9}{11}+\dfrac{12}{17}=\dfrac{12}{17}\)
a: \(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{-2}{6}=\dfrac{-1}{3}\)
b: \(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)
\(=\dfrac{2.3^9.2^9-\left(2^2\right)^5.\left(3^2\right)^4}{2^{10}.3^7+3^7.2^7.2^3.5}\\ =\dfrac{2^{10}.3^9-2^{10}.3^8}{2^{10}.3^7+3^7.2^{10}.5}\\ =\dfrac{2^{10}.3^8\left(3-1\right)}{2^{10}.3^7\left(1+5\right)}\\ =\dfrac{3.2}{6}=\dfrac{6}{6}=1\)
a) x : 12 = 10
x = 12 . 10
x = 120
b) 159 : n = 3
n = 159 : 3
n = 53
c) (x - 3) - 7 = 63
x - 3 - 7 = 63
x - 10 = 63
x = 63 + 10
x = 73
\(9^x=5\cdot9^7+5\cdot9^7\)
\(\Rightarrow9^x=9^7\cdot\left(5+4\right)\)
\(\Rightarrow9^x=9^7\cdot9\)
\(\Rightarrow9^x=9^8\)
\(\Rightarrow x=8\)
x = 8