bailey60590
bailey60590 bailey60590
  • 21-12-2020
  • Mathematics
contestada

For what value of x does
[tex]4^{x}=(\frac{1}{8})^{x + 5} [/tex]
-15
-3
3
15​

Respuesta :

LammettHash
LammettHash LammettHash
  • 01-01-2021

Write both sides as powers of 2:

[tex]4^x=(2^2)^x=2^{2x}[/tex]

[tex]\left(\dfrac18\right)^{x+5}=8^{-x-5}=(2^3)^{-x-5}=2^{-3x-15}[/tex]

Since both powers of 2 are equal, the exponents are equal:

2x = -3x - 15

5x = -15

x = -3

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