What logarithmic function represents the data in the table? x f(x) 25 2 125 3 625 4
\(\bf recall\\\\ log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad {{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y \\\\ -----------------------------\\\\ thus\qquad \begin{array}{cc|llll} x&y&5^y=x\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 25&2&5^2=25\\ 125&3&5^3=125\\ 625&4&5^4=625\\ \end{array} \\\\\\ \textit{so hmmm what would that be in log notation? }\ 5^y=x \iff \boxed{?}\)
Answer:
\(f(x) =log_5 x\)
Step-by-step explanation:
Here f(x) =2 when x = 25 that is \(5^{2}\)
f(x) = 3 when x = 125 that is \(5^{3}\)
f(x) = 4 when x =625 that is \(5^{4}\)
\(f(x) =log_5 x\)
here we can see that each value is exponent of 5
therefore function must be log function with base 5
so it is \(f(x) =log_5 x\)