55087732 55087732
  • 19-08-2022
  • Mathematics
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2^x=7; evaluate 4^(x-1)

Respuesta :

devishri1977
devishri1977 devishri1977
  • 19-08-2022

Answer:

[tex]\sf \dfrac{49}{4}[/tex]

Step-by-step explanation:

Exponent law:

     [tex]\sf \dfrac{a^m}{a^n} =a^{m-n}[/tex]

  [tex]\sf 4^{x-1}=\dfrac{4^x}{4^1}[/tex]

Write the expression 4ˣ  with base 2.

We know that 4 = 2².

[tex]\sf \dfrac{4^x}{4}=\dfrac{2^{2x}}{4}\\\\[/tex]

    [tex]\sf= \dfrac{(2^x)^2}{4}\\\\\ = \dfrac{7^2}{4}\\\\=\dfrac{49}{4}[/tex]

       

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