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iris [78.8K]
3 years ago
8

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

Mathematics
2 answers:
Ray Of Light [21]3 years ago
6 0
\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{?}
Hitman42 [59]3 years ago
5 0

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

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