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Given the functions f(x)=4x^(5) and g(x)=3^(x), which of the following statements is true? f(14)=g(14) f(14) < g(14) f(14) > g(14)

Given the functions f(x)=4x5 f(x)=4 x^{5} and g(x)=3x g(x)=3^{x} , which of the following statements is true?\newlinef(14)=g(14) f(14)=g(14) \newlinef(14)<g(14) f(14)<g(14) \newline=""f(14)="">g(14)="" f(14)="">g(14)

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Full solution

Q. Given the functions f(x)=4x5 f(x)=4 x^{5} and g(x)=3x g(x)=3^{x} , which of the following statements is true?\newlinef(14)=g(14) f(14)=g(14) \newlinef(14)<g(14) f(14)<g(14) \newlinef(14)>g(14) f(14)>g(14)
  1. Calculate f(14)f(14): Calculate f(14)f(14) using the function f(x)=4x5f(x) = 4x^5.f(14)=4×(14)5=4×537824=2151296f(14) = 4 \times (14)^5 = 4 \times 537824 = 2151296
  2. Calculate g(14)g(14): Calculate g(14)g(14) using the function g(x)=3xg(x) = 3^x.\newlineg(14)=314g(14) = 3^{14}\newline=4782969\quad = 4782969
  3. Compare f(14)f(14) and g(14)g(14): Compare f(14)f(14) and g(14)g(14) to determine which statement is true.\newlineSince f(14)=2151296f(14) = 2151296 and g(14)=4782969g(14) = 4782969, it is clear that f(14) < g(14).

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