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What is the value of x in the equation: 2^(3^x) = 10^(6^x) ?
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mhanifa

Answer:

  • [tex]log\ (log\ 2)/\ log\ 2[/tex]   or ≈ - 1.73

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Solve in below steps, using log and exponent rules:

  • [tex]2^{3^x}=10^{6^x}[/tex]                                             Given
  • [tex]log\ 2^{3^x}=log\ 10^{6^x}[/tex]                                  Log both sides
  • [tex]3^x\ log\ 2=6^x\ log\ 10[/tex]                              Log of power rule
  • [tex]3^x\ log\ 2=6^x[/tex]                                         log 10 = 1
  • [tex]3^x\ log\ 2=(3*2)^x[/tex]                                 Power of the product rule
  • [tex]3^x\ log\ 2=3^x*2^x[/tex]                                  Cancel 3ˣ on both sides
  • [tex]log\ 2=2^x[/tex]                                              Log both sides
  • [tex]log\ (log\ 2)=x\ log\ 2[/tex]                              Divide both sides by log 2
  • [tex]x=log\ (log\ 2)/\ log\ 2[/tex]                            Answer

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