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
explanation: The document contains a math question and its solution. The question is to find the value of \( x \) given the equation \( \log_x \left( \frac{1}{8} \right) = -\frac{3}{2} \). The solution is provided, and the answer is \( x = 4 \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its solution. The question is to find the value of \( x \) given the equation \( \log_x \left( \frac{1}{8} \right) = -\frac{3}{2} \). The solution is provided, and the answer is \( x = 4 \).
  
  Label: question-and-answer