Respuesta :

[tex]\\ \sf\longmapsto 2^x=5(3^{x+3}[/tex]

[tex]\\ \sf\longmapsto 2^x=5(3^x3^3)[/tex]

[tex]\\ \sf\longmapsto \dfrac{2^x}{3^x}=5(27)=135[/tex]

[tex]\\ \sf\longmapsto (\dfrac{2}{3})^x=135[/tex]

[tex]\\ \sf\longmapsto 0.6^x=135[/tex]

  • x[tex]\not{\in}[/tex]Z
Eduard22sly

The value of x in the expression is –12.1

Data obtained from the question

  • 2^x = 5 × 3^(x+3)
  • Value of x =?

How to determine the value of x

2^x = 5 × 3^(x+3)

Recall

M^(a+c) = M^a × M^c

Thus,

3^(x+3) = 3^x × 3^3

Therefore,

2^x = 5 × 3^(x+3)

2^x = 5 × 3^x × 3^3

2^x = 5 × 3^x × 27

2^x =  3^x × 135

Divide both side by 3^x

(2/3)^x = 135

Take the log of both side

Log (2/3)^x = Log 135

xLog (2/3) = Log 135

Divide both side by Log (2/3)

x = Log 135 / Log (2/3)

x = –12.1

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