Respuesta :

Answer:

[tex]x=8.83[/tex]

Step-by-step explanation:

  • Initial equation: [tex]16= 86 (0.83^x)[/tex]
  • Dividing both sides by 86 leads you to [tex] \frac{16}{86} = 0.83^{x} [/tex] which is equal to [tex] 0.1927 = 0.83^{x} [/tex]
  • Then, all you have to do is take natural logarithm both sides: [tex]ln (0.1927) = x ln (0.83)[/tex] which is a result of applying natural logarithm properties (particulary the property that affirms that [tex]ln (m^n) = n \plus {ln(m)}[/tex])
  • Finally, [tex]x = \frac{ln( 0.1927)}{ln(0.83)} = 8.83[/tex].