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]
