jessygonzalez8607 jessygonzalez8607
  • 22-10-2019
  • Mathematics
contestada

If x and y are positive real numbers, and log(y) = 3 + 2 log(x), express y in terms of x.

Respuesta :

carlos2112
carlos2112 carlos2112
  • 22-10-2019

Answer:

[tex]y=e^{3}*x^{2}[/tex]

Step-by-step explanation:

First, use reduction of power property:

[tex]log(x^{y} )=ylog(x)[/tex]

So:

[tex]log(y)=3+log(x^{2} )[/tex]

Cancel logarithms by taking exp of both sides:

[tex]e^{log(y)} =e^{3+logx^{2} }[/tex]

Keep in mind this:

[tex]x^{y} *x^{z} =x^{y+z}[/tex]

Hence:

[tex]y=e^{3} *e^{log(x^{2} )} =e^{3} *x^{2}[/tex]

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