Question

What logarithmic function represents the data in the table? x f(x) 25 2 125 3 625 4

Answer 1

`\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 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 2

`f(x) =log_5 x`

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`