smccarthy15 smccarthy15
  • 24-02-2020
  • Mathematics
contestada

The question is in the image below. I need help with this as soon as possible. Thank you!!!

The question is in the image below I need help with this as soon as possible Thank you class=

Respuesta :

kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 01-03-2020

Answer:

[tex]x = - 1.60[/tex]

Step-by-step explanation:

We want to solve

[tex] {4}^{x + 3} = 7[/tex]

using change of base formula.

First we take antilog to get;

[tex]x + 3 = log_{4}(7) [/tex]

The formula is:

[tex] log_{b}(y) = \frac{ log(y) }{ log(b) } [/tex]

We apply apply the change of base formula on the right to get:

[tex]x + 3 = \frac{ log(7) }{ log(4) } [/tex]

[tex]x + 3 = 1.40[/tex]

Subtract 3 from both side to get:

[tex]x = 1.4 - 3 = - 1.6[/tex]

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