mimibimitheanimator
mimibimitheanimator mimibimitheanimator
  • 24-03-2021
  • Mathematics
contestada

(1/2)^x=16^2

Could you please help me with the step-by step? This problem is giving me trouble. ​

12x162Could you please help me with the stepby step This problem is giving me trouble class=

Respuesta :

LammettHash
LammettHash LammettHash
  • 24-03-2021

Write both sides as powers of 2. First,

1/2 = 2⁻¹

16 = 2⁴

so the equation can be rewritten as

(1/2)ˣ = 16²

(2⁻¹)ˣ = (2⁴)²

Recall that [tex](a^b)^c=a^{bc}[/tex], so that

2⁻ˣ = 2⁸

The bases are the same, so the exponents must be equal:

-x = 8

x = -8

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