text: # explain the solving of equationexplain how to deal with an exponential equation where bases are not the same. a^x=b
  
  Asked on by frontman0
  
  justaguide | College Teacher | (Level 2) Distinguished Educator
  
  Posted on
  
  To solve an equation of the form a^x = b where the bases are not the same we cannot equate the exponents.
  
  Instead logarithms can be used
  
  log a^x = log b
  
  use the property log a^x = x*log a
  
  => x*log a = log b
  
  => x = log b / log a
  
  The solution of these kind of equations is log b/ log a
  
  giorgiana1976 | College Teacher | (Level 3) Valedictorian
  
  Posted on
  
  One example:
  
  3^(x-3)=17
  
  To determine x, we'll take log on both sides:
  
  log 3^(x-3)=log 17
  
  We'll use the power rule of logarithms:
  
  (x-3)*log 3 = log 17
  
  We'll divide by log 3 both sides of the equation:
  
  (x-3) = log 17 / log 3
  
  We'll add 3  both sides:
  
  x = log 17 / log 3 + 3
  
  We'll compute the ratio log 17 / log 3 + 3:
  
  log 17 / log 3 = 1.2304/0.4771 + 3
  
  x = 2.6617/0.4771
  
  x = 5.5789 approx.
  
  frontman0 | Student, Undergraduate | (Level 1) Honors
  
  Posted on
  
  provide a practical example of such a problem
explanation: The document contains a math question and multiple answers to the question. The question asks how to solve an exponential equation where the bases are not the same, specifically \( a^x = b \). The document provides two detailed answers explaining the process of solving such equations using logarithms.
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: # explain the solving of equationexplain how to deal with an exponential equation where bases are not the same. a^x=b
  
  Asked on by frontman0
  
  justaguide | College Teacher | (Level 2) Distinguished Educator
  
  Posted on
  
  To solve an equation of the form a^x = b where the bases are not the same we cannot equate the exponents.
  
  Instead logarithms can be used
  
  log a^x = log b
  
  use the property log a^x = x*log a
  
  => x*log a = log b
  
  => x = log b / log a
  
  The solution of these kind of equations is log b/ log a
  
  giorgiana1976 | College Teacher | (Level 3) Valedictorian
  
  Posted on
  
  One example:
  
  3^(x-3)=17
  
  To determine x, we'll take log on both sides:
  
  log 3^(x-3)=log 17
  
  We'll use the power rule of logarithms:
  
  (x-3)*log 3 = log 17
  
  We'll divide by log 3 both sides of the equation:
  
  (x-3) = log 17 / log 3
  
  We'll add 3  both sides:
  
  x = log 17 / log 3 + 3
  
  We'll compute the ratio log 17 / log 3 + 3:
  
  log 17 / log 3 = 1.2304/0.4771 + 3
  
  x = 2.6617/0.4771
  
  x = 5.5789 approx.
  
  frontman0 | Student, Undergraduate | (Level 1) Honors
  
  Posted on
  
  provide a practical example of such a problem
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and multiple answers to the question. The question asks how to solve an exponential equation where the bases are not the same, specifically \( a^x = b \). The document provides two detailed answers explaining the process of solving such equations using logarithms.
  
  Label: question-and-answer