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Given the functions f(x)=5x^(5) and g(x)=9*6^(x), which of the following statements is true? f(4) < g(4) f(4) > g(4) f(4)=g(4)

Given the functions f(x)=5x5 f(x)=5 x^{5} and g(x)=9⋅6x g(x)=9 \cdot 6^{x} , which of the following statements is true?\newlinef(4)<g(4) f(4)<g(4) \newline=""f(4)="">g(4)="" f(4)="">g(4) \newlinef(4)=g(4) f(4)=g(4)

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Full solution

Q. Given the functions f(x)=5x5 f(x)=5 x^{5} and g(x)=9⋅6x g(x)=9 \cdot 6^{x} , which of the following statements is true?\newlinef(4)<g(4) f(4)<g(4) \newlinef(4)>g(4) f(4)>g(4) \newlinef(4)=g(4) f(4)=g(4)
  1. Calculate f(4)f(4): Calculate f(4)f(4) using the function f(x)=5x5f(x) = 5x^{5}.\newlinef(4)=5×45f(4) = 5 \times 4^{5}\newline =5×1024= 5 \times 1024\newline =5120= 5120
  2. Calculate g(4)g(4): Calculate g(4)g(4) using the function g(x)=9×6xg(x) = 9 \times 6^{x}.g(4)=9×64 =9×1296 =11664g(4) = 9 \times 6^{4}\ = 9 \times 1296\ = 11664
  3. Compare values: Compare the values of f(4)f(4) and g(4)g(4). Since f(4)=5120f(4) = 5120 and g(4)=11664g(4) = 11664, it is clear that f(4) < g(4).

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