text: # What is x if log(x) (1/8) = -3/2.
  
  Posted on
  
  We have log(x) (1/8) = -3/2. We have to determine x.
  
  log(x) (1/8) = -3/2
  
  => (1/8) = x^(-3/2)
  
  => (1/2)^3 = x^(-3/2)
  
  => (1/4)^(3/2) = x^(-3/2)
  
  => 4^(-3/2) = x^(-3/2)
  
  As the exponent are equal we can equate the base.
  
  => x = 4
  
  The required value of x is x = 4.
  
  Posted on
  
  Given that log(x) (1/8) = -3/2
  
  We need to find the values of x.
  
  ==> Let us simplify.
  
  First we will rewrite (1/8) = (1/2)^3
  
  ==> (1/2)^3 = 2^-3
  
  ==> log(x) 2^-3 = -3/2
  
  Now we know that log a^b = b*log a
  
  ==> log(x) 2^-3 = -3*log(x) 2 = -3/2
  
  We will divide by -3.
  
  ==> log(x) 2 = -3/2*-3 = 1/2
  
  Now we will rewrite using exponent form.
  
  ==> x^1/2 = 2
  
  We will square both sides.
  
  ==> x = 4