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\(\left(\frac{1}{2}\right)^5\times x=\left(\frac{1}{2}\right)^7\)
\(x=\left(\frac{1}{2}\right)^7\div\left(\frac{1}{2}\right)^5\)
\(x=\left(\frac{1}{2}\right)^{7-5}=\left(\frac{1}{2}\right)^2=\frac{1}{4}\) .
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{9}{21}\right)^2\)
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{3}{7}\right)^4\)
\(x=\left(\frac{3}{7}\right)^4\div\left(\frac{3}{7}\right)^2\)
\(x=\left(\frac{3}{7}\right)^{4-2}=\left(\frac{3}{7}\right)^2=\frac{9}{49}\)
\(2^x=2\Rightarrow x=1\)
\(3^x=3^4\Rightarrow x=4\)
\(7^x=7^7\Rightarrow x=7\)
\(\left(-3\right)^x=\left(-3\right)^5\Rightarrow x=5\)
\(\left(-5\right)^x=\left(-5\right)^4\Rightarrow x=4\)
\(2^x=4\Leftrightarrow2^x=2^2\Rightarrow x=2\)
\(2^x=8\Leftrightarrow2^x=2^3\Rightarrow x=3\)
\(2^x=16\Leftrightarrow2^x=2^4\Rightarrow x=4\)
\(3^{x+1}=3^2\Leftrightarrow x+1=2\Leftrightarrow x=2-1\Rightarrow x=1\)
\(5^{x-1}=5\Leftrightarrow x-1=1\Leftrightarrow x=1+1\Rightarrow x=2\)
\(6^{x+4}=6^{10}\Leftrightarrow x+4=10\Leftrightarrow x=10-4\Rightarrow x=6\)
\(5^{2x-7}=5^{11}\Leftrightarrow2x-7=11\Leftrightarrow2x=11+7\Leftrightarrow2x=18\Leftrightarrow x=18\div2\Rightarrow x=9\)
\(\left(-2\right)^{4x+2}=64\)
\(2^{-4x+2}=2^6\Leftrightarrow-4x+2=6\Leftrightarrow-4x=6-2\Leftrightarrow-4x=4\Leftrightarrow x=4\div\left(-4\right)\Rightarrow x=-1\)
\(\left(\frac{1}{2}\right)^x=\left(\frac{1}{2}\right)^5\Rightarrow x=5\)
\(\left(\frac{5}{6}\right)^{2x}=\left(\frac{5}{6}\right)^5\Rightarrow2x=5\Rightarrow x=\frac{5}{2}\)
\(\left(\frac{3}{4}\right)^{2x-1}=\left(\frac{3}{4}\right)^{5x-4}\Rightarrow2x-1=5x-4\)
\(2x-5x=-4+1\)
\(-3x=-3\Rightarrow x=1\)
\(\left(\frac{-1}{10}\right)^x=\frac{1}{100}\)
\(\left(\frac{1}{10}\right)^{-x}=\left(\frac{1}{10}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{2}\right)^x=\frac{9}{4}\)
\(\left(\frac{3}{2}\right)^{-x}=\left(\frac{3}{2}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{5}\right)^{2x}=\frac{9}{25}\)
\(\left(\frac{3}{5}\right)^{-2x}=\left(\frac{3}{5}\right)^2\Rightarrow-2x=2\Rightarrow x=-1\)
\(\left(\frac{-2}{3}\right)^x=\frac{-8}{27}\)
\(\left(\frac{-2}{3}\right)^x=\left(\frac{-2}{3}\right)^3\Rightarrow x=3\).
hehe.
đánh tới què tay, hoa mắt lun r nekkk!!
a)
\((3x-7)^5=0\Rightarrow 3x-7=0\Rightarrow x=\frac{7}{3}\)
b)
\(\frac{1}{4}-(2x-1)^2=0\)
\(\Leftrightarrow (2x-1)^2=\frac{1}{4}=(\frac{1}{2})^2=(-\frac{1}{2})^2\)
\(\Rightarrow \left[\begin{matrix} 2x-1=\frac{1}{2}\\ 2x-1=\frac{-1}{2}\end{matrix}\right.\Rightarrow \Rightarrow \left[\begin{matrix} x=\frac{3}{4}\\ x=\frac{1}{4}\end{matrix}\right.\)
c)
\(\frac{1}{16}-(5-x)^3=\frac{31}{64}\)
\(\Leftrightarrow (5-x)^3=\frac{1}{16}-\frac{31}{64}=\frac{-27}{64}=(\frac{-3}{4})^3\)
\(\Leftrightarrow 5-x=\frac{-3}{4}\)
\(\Leftrightarrow x=\frac{23}{4}\)
d)
\(2x=(3,8)^3:(-3,8)^2=(3,8)^3:(3,8)^2=3,8\)
\(\Rightarrow x=3,8:2=1,9\)
e)
\((\frac{27}{64})^9.x=(\frac{-3}{4})^{32}\)
\(\Leftrightarrow [(\frac{3}{4})^3]^9.x=(\frac{3}{4})^{32}\)
\(\Leftrightarrow (\frac{3}{4})^{27}.x=(\frac{3}{4})^{32}\)
\(\Leftrightarrow x=(\frac{3}{4})^{32}:(\frac{3}{4})^{27}=(\frac{3}{4})^5\)
f)
\(5^{(x+5)(x^2-4)}=1\)
\(\Leftrightarrow (x+5)(x^2-4)=0\)
\(\Leftrightarrow \left[\begin{matrix} x+5=0\\ x^2-4=0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x+5=0\\ x^2=4=2^2=(-2)^2\end{matrix}\right.\)
\(\Rightarrow \left[\begin{matrix} x=-5\\ x=\pm 2\end{matrix}\right.\)
g)
\((x-2,5)^2=\frac{4}{9}=(\frac{2}{3})^2=(\frac{-2}{3})^2\)
\(\Rightarrow \left[\begin{matrix} x-2,5=\frac{2}{3}\\ x-2,5=\frac{-2}{3}\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{19}{6}\\ x=\frac{11}{6}\end{matrix}\right.\)
h)
\((2x+\frac{1}{3})^3=\frac{8}{27}=(\frac{2}{3})^3\)
\(\Rightarrow 2x+\frac{1}{3}=\frac{2}{3}\Rightarrow x=\frac{1}{6}\)
a)
\(3(2x-\frac{1}{2})+2(\frac{3}{8}-x)=2,75\)
\(\Leftrightarrow 6x-\frac{3}{2}+\frac{3}{4}-2x=2,75\)
\(\Leftrightarrow 4x=\frac{7}{2}\Rightarrow x=\frac{7}{8}\)
b)
\(x-\frac{1}{3}(5-3x)=1\frac{1}{2}x+5\frac{1}{2}\)
\(\Leftrightarrow x-\frac{5}{3}+x=x+\frac{1}{2}x+\frac{11}{2}\)
\(\Leftrightarrow \frac{1}{2}x=\frac{43}{6}\) \(\Rightarrow x=\frac{43}{3}\)
c) \(\sqrt{x-1}=4\Rightarrow x-1=4^2\Rightarrow x=4^2+1=17\)
d)
\(|x|-5\frac{3}{7}|-x|-\frac{3}{4}=2|x|-1\frac{1}{7}\)
\(\Leftrightarrow |x|-\frac{38}{7}|x|-\frac{3}{4}=2|x|-\frac{8}{7}\)
\(\Leftrightarrow |x|(1-\frac{38}{7}-2)=\frac{3}{4}-\frac{8}{7}\)
\(\Leftrightarrow |x|.\frac{-45}{7}=\frac{-11}{28}\)
\(\Leftrightarrow |x|=\frac{11}{180}\Rightarrow \left[\begin{matrix} x=\frac{11}{180}\\ x=-\frac{11}{180}\end{matrix}\right.\)
a.\(3^{x-1}=243\)
\(3^x:3^1=243\)
\(3^x=729\)
\(\Leftrightarrow3^6=729\)
\(\Leftrightarrow x=6\)
b.\(\left(\dfrac{2}{3}\right)^{x+1}=\dfrac{8}{4}\)
\(\left(\dfrac{2}{3}\right)^x.\left(\dfrac{2}{3}\right)=\dfrac{8}{4}\)
\(\left(\dfrac{2}{3}\right)^x=3\)
Câu b tính đến đây rồi không mò đc x nữa.
Mình quên ghi đề bài là tìm giá trị nhỏ nhất của các biểu thức sau
a) F(x) + Q(x) = ( x^2 + 3x^2 + 3x - 2 ) + ( - x^3 - x^2 - 5x + 2 )
= x^2 + 3x^2 + 3x - 2 - x^3 - x^2 - 5x + 2
= ( x^2 - x^2 +3x^2 ) + ( 3x - 5x ) + ( -2 + 2 )
= 3x^2 - 2x
b) F(x) - Q(x) = ( x^2 + 3x^2 + 3x - 2 ) - ( - x^3 - x^2 - 5x + 2 )
= x^2 + 3x^2 x+ 3x - 2 + x^3 + x^2 + 5x - 2
= ( x^2 + x^2 + 3x^2 ) + ( 3x + 5x ) + ( -2 - 2 )
= 5x^2 + 8x - 4
a) C = 20013 - |5−2x|
do \(-\left|5-2x\right|\le0\forall x\)
=> 20013-\(\left|5-2x\right|\le20013\)
=>A≤20013
=> GTLN C =20013 khi 5-2x=0
=> 2x=5
=> x=\(\dfrac{5}{2}\)
vậy GTLN C = 20013 khi x=\(\dfrac{5}{2}\)
b) D = 7 - \(\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\)
do \(-\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\le0\forall x\)
=> 7-\(\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\le7\)
=> D≤7
=> GTLN D =7 khi \(\dfrac{2}{3}+\dfrac{1}{4}x=0\)
=> x=-\(\dfrac{8}{3}\)
bn ghi rõ đâu bài ra chứ mk ko bt câu nào là GTNN câu nào là GTLN đâu
giá trị nhỏ nhất hoặc giá trị lớn nhất