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\(3^{x-1}=\frac{1}{243}\)
\(\Rightarrow3^x=243\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)
720 : [ 4x - ( 2x - 5) ] = 23 . 5
720 : (4x - 2x + 5) = 8 . 5
720 : (2x + 5) = 40
2x + 5 = 720 : 40
2x + 5 = 18
2x = 18 - 5
2x = 13
x = 13/2
Ta có:
\(5^{299}< 5^{300}=\left(5^3\right)^{100}=125^{100}\)
\(3^{501}>3^{500}=\left(3^5\right)^{100}=243^{100}\)
Vì \(125^{100}< 243^{100}\) nên \(5^{299}< 125^{100}< 243^{100}< 3^{501}\) hay \(5^{299}< 5^{501}\)
Vậy \(5^{299}< 3^{501}\)
Mình chỉ biết làm câu b thôi. Xl nhé!
b/ \(2^x=32^5.64^6\)
\(\Rightarrow2^x=\left(2^5\right)^5.\left(2^6\right)^6\)
\(\Rightarrow2^x=2^{25}.2^{36}\)
\(\Rightarrow2^x=2^{25+36}\)
\(\Rightarrow2^x=2^{61}\)
\(\Rightarrow x=61\)
Vậy \(x=61\)
a, Ta có: \(\left(\dfrac{1}{80}\right)^7>\left(\dfrac{1}{81}\right)^7=\left(\dfrac{1}{3^4}\right)^7=\left(\dfrac{1}{3}\right)^{28}=\dfrac{1}{3^{28}}\)
\(\left(\dfrac{1}{243}\right)^6=\left(\dfrac{1}{3^5}\right)^6=\left(\dfrac{1}{3}\right)^{30}=\dfrac{1}{3^{30}}\)
Vì \(\dfrac{1}{3^{28}}>\dfrac{!}{3^{30}}\Rightarrow\left(\dfrac{1}{81}\right)^7>\left(\dfrac{1}{243}\right)^6\Rightarrow\) \(\left(\dfrac{1}{80}\right)^7>\left(\dfrac{1}{243}\right)^6\)
b, Ta có: \(\left(\dfrac{3}{8}\right)^5=\dfrac{3^5}{\left(2^3\right)^5}=\dfrac{243}{2^{15}}>\dfrac{243}{3^{15}}>\dfrac{125}{3^{15}}=\dfrac{5^3}{\left(3^5\right)^3}=\left(\dfrac{5}{243}\right)^3\)
\(\Rightarrow\left(\dfrac{3}{8}\right)^5>\left(\dfrac{5}{243}\right)^3\)
( 4.2 )5 : ( 23.1/6 ) = ( 21/5 )5 : ( 8.1/6 )
= ( )
cho mk xin lỗi nha
mk định hủy