Question

Which system of equations could be graphed to solve the equation below? log0.5x=log32 +x

Answer 1

Explanation:

The system of equation to be graphed is the following :

f(x) = Log_0.5 x

f(x) = Log_{3} (2 + x)

And the solution is the intersection point of the two graphs.

Check attachment for point of intersection.

Answer 2

y1 = (Log x)/(Log 0.5)

y2 = [(Log 2)/(Log 3)] + x

Option D

Explanation:

We are given;

Log_0.5_x = (Log_3_2) + x

To solve the equation graphically, we have to plot the graphs of these two functions and find the point of intersection of these graphs.

Using: log_a b = log b / log a

1) a = x, b=0.5

So, y1 = log0.5 x

Which gives; y1= (log x)/(log0.5)

2) a=2, b=3

So, y2 = (log_3 2) + x

So, y2 = (log 2 / log 3) +x

Hence, appropriate system is;

y1 = (Log x)/(Log 0.5)

And y2 = [(Log 2)/(Log 3)] + x

Looking at the options in the image attached, the correct solution that corresponds to our answer is Option D