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

Given the functions f(x)=5x4 f(x)=5 x^{4} and g(x)=4⋅3x g(x)=4 \cdot 3^{x} , which of the following statements is true?\newlinef(3)=g(3) f(3)=g(3) \newlinef(3)<g(3) f(3)<g(3) \newline=""f(3)="">g(3)="" f(3)="">g(3)

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Full solution

Q. Given the functions f(x)=5x4 f(x)=5 x^{4} and g(x)=4⋅3x g(x)=4 \cdot 3^{x} , which of the following statements is true?\newlinef(3)=g(3) f(3)=g(3) \newlinef(3)<g(3) f(3)<g(3) \newlinef(3)>g(3) f(3)>g(3)
  1. Calculate f(3)f(3): Calculate f(3)f(3) using the function f(x)=5x4f(x)=5x^{4}.\newlinef(3) = 5 \times (3)^4\(\newline = 5 \times 81\newline = 405\)
  2. Calculate g(3)g(3): Calculate g(3)g(3) using the function g(x)=4⋅3xg(x)=4\cdot3^{x}.g(3)=4⋅33=4⋅27=108g(3) = 4 \cdot 3^{3} = 4 \cdot 27 = 108
  3. Compare values: Compare the values of f(3)f(3) and g(3)g(3).\newlineSince f(3)=405f(3) = 405 and g(3)=108g(3) = 108, we can see that f(3) > g(3).

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