Question

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Given the functions f(x) and g(x) below, find
all solutions to the equation f(x) = g(x)
graphically to the nearest hundredth.
f(x) = ln (8x + 10) + 1
g(x) = 3

Answer 1

Okay, let's solve this step-by-step:

* f(x) = ln (8x + 10) + 1

* g(x) = 3

* Set them equal: ln (8x + 10) + 1 = 3

* Subtract 1 from both sides: ln (8x + 10) = 2

* Take the inverse ln of both sides: 8x + 10 = e^2

* Subtract 10 from both sides: 8x = e^2 - 10

* Divide both sides by 8: x = (e^2 - 10) / 8

* Evaluate: x = 0.39

* Round to the nearest hundredth: x = 0.39

Therefore, the solution to f(x) = g(x) is x = 0.39.

Answer 2

The solution is to the f(x) = g(x) y = 3.30 and x = 0.

How to solve equations graphically.

Table for the function f(x) = ln(8x + 10) + 1 is form as follows

| x| f(x)

|-------|--------

| 0 | 1

| 1 | 3.890

| 2 | 4.258

| -1 | 1.693

The graph of f(x) = ln(8x + 10) + 1 is a logarithmic curve with a vertical shift. It approaches negative infinity as x approaches -5/4 and increases without bound as x goes to infinity.

g(x) is a straight parallel to x-axis. The intersection of the curves gives the solutions to the equations

From the graph the point of intersection is

(0,3.30)

The solution is

y = 3.30 and x = 0.