Question

See the attachments below!!!

Answer 1

Answer:

1) x=0.465

2) option A.

Step-by-step explanation:

1) The given equation is:

${3}^{x + 2} = 15$We rewrite this as logarithm to get:

$x + 2 = log_{3}(15)$

The change of base formula is:

$log_{b}(y) = \frac{ log(y) }{ log(b) }$

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

$x + 2 = \frac{ log(15) }{ log(3) }$

$x + 2 = \frac{1.176}{0.477}$

$x + 2 = 2.465$

Group similar terms:

$x = 2.465 - 2.000 = 0.465$

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.