Question

Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the equation?

Answer 1

Answer:

The solution to the given equation is at point (1.353, 1.613).        

Step-by-step explanation:

Given : Kim solved the equation below by graphing a system of equations.

$\log_2(3x-1)=\log_4(x+8)$

To find : What is the approximate solution to the equation?

Solution :

Let, $y_1=\log_2(3x-1)$

and  $y_2=\log_4(x+8)$

Now, we plot these two equations.

The graph of $y_1=\log_2(3x-1)$ is shown with green line.

The graph of $y_2=\log_4(x+8)$ is shown with violet line.

The solution to this system will be their intersection point.

The intersection point of these graph is (1.353, 1.613)

Refer the attached graph below.

Therefore, The solution to the given equation is at point (1.353, 1.613).

Answer 2

Answer:

(1.35, 1.6)

Step-by-step explanation:

A screenshot of the graph is attached.

Once we graph the equations $y=\log_2(3x-1)$ and $y=\log_4(x+8)$, the solution to this system will be their intersection point.

Tracing the graph on the calculator, we see that the point of intersection is at about (1.35, 1.6).