Question

1. Tìm x, biết:
a) \(\left(x-\frac{3}{4}\right)^2=0\)

b) \(\left(x+\frac{1}{2}\right)^2=\frac{9}{64}\)

c) \(\frac{\left(-2\right)^x}{16}=-8\)
2. Tính: 
  \(\frac{6^3.12^4}{4^7.9^5}\)
3. Tìm \(x\in N\), biết:
   \(3^2.81\le3^x\le27.243\)

     

Answer 1

1. Tìm x, biết :

a. ( x - \(\frac{3}{4}\)) \(^2\)= 0

=> x - \(\frac{3}{4}\)= 0

=> x = 0 + \(\frac{3}{4}\)

=> x = \(\frac{3}{4}\)

b. ( x + \(\frac{1}{2}\)) \(^2\)= \(\frac{9}{64}\)

=> ( x + \(\frac{1}{2}\)) \(^2\)= ( \(\frac{3}{8}\)) \(^2\)

=> x + \(\frac{1}{2}\)= \(\frac{3}{8}\)

=> x = \(\frac{3}{8}\)- \(\frac{1}{2}\)

=> x = \(\frac{-1}{8}\)

c.  \(\frac{\left(-2\right)^x}{16}=-8\)

=> \(\frac{\left(-2\right)^x}{16}=\frac{-8}{1}=\frac{-128}{16}\)

=> ( -2)\(^x\)= -128

=> ( -2 ) \(^x\)= ( -2) \(^7\)

=> x = 7