Question

Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. Select all that apply. f(x)=8^(x-9) g(x)=log(3x)+2

a. (0,0)
b. (9.2, 1.5)
c. (9.6, 3.5)
d. (5.3, 9.8)
e. (3.5, 9.6)

Answer 1

c. (9.6 , 3.5)

Explanation:

To solve this problem, we are gonna use a function graph tool, in order to get the result rounded to the nearest tenth, as the problem mentioned.

The given function that form the system are

`f(x)=8^((x-9))`

`g(x)=log(3x)+2`

In the image attached is included both function. The interception point of both curves represents the solution of the system. Remember that the solution of a system, using graphic methods, it's the interception point.

According to the graph, the solution, rounded to the nearest tenth, is (9.6 , 3.5).

Therefore, the right choice is C.

Answer 2

We can use using graphing technology to solve the system of equations here.

So draw sketch of graphs
`y = 8^((x-9))` and
`y = log (3x) +2` on graphing calculator. you will get sketch as shown

Take pointer to point of intersection as shown. It displays (x,y) coordinate of points of intersection as (9.597, 3.459) as show in figure.

Now round off these values to nearest tenth thats one digit after decimal dot.

so to round 9.597 to one decimal place we will see 2nd decimal digit(next to place where you have to round off) which is 9 here and as 9 is greater than 5 so we will increase 1st decimal place digit by 1, so round to one decimal place will be 9.6.

Similarly to round off 3.459 to one decimal place we will see 2nd decimal digit which is 5. Again as its equals 5 we will increase the 1st decimal digit by 1 for round off. So final round off to one decimal place will be 3.5

So final answer for solution set will be choice C (9.6, 3.5)