Answer:
1) x=0.465
2) option A.
Step-by-step explanation:
1) The given equation is:
[tex] {3}^{x + 2} = 15[/tex]We rewrite this as logarithm to get:
[tex]x + 2 = log_{3}(15) [/tex]
The change of base formula is:
[tex] log_{b}(y) = \frac{ log(y) }{ log(b) } [/tex]
We apply the change of base formula on the RHS to get:
[tex]x + 2 = \frac{ log(15) }{ log(3) } [/tex]
[tex]x + 2 = \frac{1.176}{0.477} [/tex]
[tex]x + 2 = 2.465[/tex]
Group similar terms:
[tex]x = 2.465 - 2.000 = 0.465[/tex]
2)
From the graph, the logarithmic function approaches negative infinity as x approaches -6.
Therefore the vertical asymptote is x=-6
The graph touches the x-axis at x=-5, therefore the x-intercept is x=-5.
The correct answer is A.
