1. find the exact solution to the equation. 6-log8(x+7) = 5 a) x = 15 b) x = 1 c) x = 2 d) x = -1 2. find the exact solution to the equation. (5 points) one hundred times one fifth to the power of quantity x divided by four equals four. a) x = one divided by two b) x = 8 c) x = 2 d) x = 9 3. determine the function which corresponds to the given graph. a natural logarithmic function crossing the x axis at negative four and going through the point 1,2. the asymptote is x = -5

1. The equation is 

Rearranging, we have We know that (x+7) must be 8, since , so we set the equation:

                                               x+7=8, which means that x=1.

(quick check:

2.
The equation is 

Dividing both sides by 100, the right hand side becomes 1/25, which can be written as . 

Now that both exponential expressions have the same base, we set the exponents equal:

, which gives us x=8.

3.

The most well known natural logarithmic function is  (that is: .)

The asymptote of this function is the line x=0. This means that we have to shift 5 units left, to get:

                                         

Now, at 1, this function takes the value To make the function pass through (1, 2), we could multiply by 

So, the function would be

Answers:

 1. 1

 2. 8

 3.