msmalakmohamed2 msmalakmohamed2
  • 15-06-2022
  • Mathematics
contestada

2ⁿ+2ⁿ+2ⁿ+2ⁿ=2¹⁶
value of n?​

Respuesta :

loneguy
loneguy loneguy
  • 15-06-2022

Answer:

[tex]n = 14[/tex]

Step-by-step explanation:

[tex]~~~~~~~2^n+2^n+2^n+2^n = 2^{16}\\\\\implies 4 \cdot 2^n = 2^{16}\\\\\implies 2^2 \cdot 2^n = 2^{16}\\\\\implies 2^{n+2} = 2^{16}~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies n+ 2 = 16\\\\\implies n = 16-2 \\\\\implies n = 14[/tex]

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