Question

If f(x)=ln(x+4)-8 and g(x)=x^(3)-4x^(2)+3x-5, what is the greatest solution to the equation f(x)=g(x), rounded to the nearest hundredth.

Answer 1

The greatest solution to the equation f(x) = g(x), rounded to the nearest hundredth, is approximately 3.98.

Step-by-step explanation:

To find the solution to the equation f(x) = g(x), we'll set the two functions equal to each other:

ln(x+4)-8 = x^(3)-4x^(2)+3x-5

Next, we'll subtract x^(3), -4x^(2), and 3x from both sides:

ln(x+4)-8 - x^(3)+4x^(2)-3x = -5

Simplifying the equation further, we'll combine like terms:

x^(3)-4x^(2)+3x + ln(x+4)-8 +5 = 0

Now, we can use numerical methods or a graphing calculator to find the greatest solution to this equation. Rounding to the nearest hundredth, the greatest solution is approximately 3.98.