VigorousCoast3988 VigorousCoast3988
  • 22-10-2019
  • Mathematics
contestada

92. Solve each equation. Express your answer as a logarithm, and then approximate the solution to the nearest thousandth.
b. 362(10t/12)=500

Respuesta :

wagonbelleville wagonbelleville
  • 22-10-2019

Answer:

t = 1.266

Step-by-step explanation:

given equation

[tex]362^{\dfrac{10t}{12}} = 500[/tex]

taking log both side in the above equation

[tex]\dfrac{10t}{12} ln (362) = ln (500)[/tex]

[tex]10 t (ln (362)) = 12 (ln (500))[/tex]

[tex]t = \dfrac{12 (ln (500))}{10(ln (362))}[/tex]

[tex]t = \dfrac{1.2 (ln (500))}{(ln (362))}[/tex]

t = 1.2 × 1.055

t = 1.266

hence, the answer of the solution is t = 1.266

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