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Given the functions f(x)=x^(4) and g(x)=2*3^(x), which of the following statements is true? f(8)=g(8) f(8) > g(8) f(8) < g(8)

Given the functions f(x)=x4 f(x)=x^{4} and g(x)=2⋅3x g(x)=2 \cdot 3^{x} , which of the following statements is true?\newlinef(8)=g(8) f(8)=g(8) \newline f(8)>g(8) \newline\( f(8)

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Q. Given the functions f(x)=x4 f(x)=x^{4} and g(x)=2⋅3x g(x)=2 \cdot 3^{x} , which of the following statements is true?\newlinef(8)=g(8) f(8)=g(8) \newlinef(8)>g(8) f(8)>g(8) \newlinef(8)<g(8) f(8)<g(8)
  1. Calculate f(8)f(8): Calculate f(8)f(8) using the function f(x)=x4f(x) = x^4.\newlinef(8)=84f(8) = 8^4\newlinef(8)=4096f(8) = 4096
  2. Calculate g(8)g(8): Calculate g(8)g(8) using the function g(x)=2×3xg(x) = 2 \times 3^x.\newlineg(8)=2×38g(8) = 2 \times 3^8\newlineg(8)=2×6561g(8) = 2 \times 6561\newlineg(8)=13122g(8) = 13122
  3. Compare values: Compare the values of f(8)f(8) and g(8)g(8). Since f(8)=4096f(8) = 4096 and g(8)=13122g(8) = 13122, it is clear that f(8) < g(8).

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