Question

Let f (x) = log₃(x) + 3 and g(x) = log3(x³) – 1.

Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form.

Part B: Determine the solution to the system of nonlinear equations.

Answer 1

Answer:

• a) h(x) = 4log₃(x) + 2
• b) x = 9

Step-by-step explanation:

Given:

• f(x) = log₃(x) + 3
• g(x) = log₃(x³) – 1

Part A

Find h(x) = f(x) + g(x)

• h(x) =
• log₃(x) + 3 + log3(x³) – 1 =
• log₃(x) + 3log₃(x) + 2 =
• 4log₃(x) + 2

Part B

Assumed f(x) and g(x) system is to be solved.

Substitute log₃(x) = y, then:

• f(x) = y + 3
• g(x) = 3y - 1

Set them equal and solve for y:

• y + 3 = 3y - 1
• 3y - y = 3 + 1
• 2y = 4
• y = 2

Substitute back:

• log₃(x) = 2 ⇒ x = 3² ⇒ x = 9

Answer 2

Answer:

Part A: log3(x^4)+2

Part b: x=9

Step-by-step explanation:

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