Suppose f(x) = loga(x) and f(7) = 2. Find f(343)

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Suppose f(x) = loga(x) and f(7) = 2. Find f(343)

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Euphemia 1 week 2021-07-20T04:30:52+00:00 1 Answers 1 views 0

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    2021-07-20T04:32:41+00:00

    Answer:

    6

    Step-by-step explanation:

    The given function to us is ,

    \rm\implies f(x)= log_a(x)

    And its value at 7 is 2 , that is ,

    \rm\implies f(x)= log_a(7) =2

    Taking this ,

    \rm\implies 2= log_a(7)

    In general we know that ,

    \bf\to log_a b = c ,\  then \ a^c = b

    Using this , we have ,

    \rm\implies a^2 = 7

    Squarerooting both sides ,

    \rm\implies a =\sqrt{ 7 }

    Therefore , when x is 343 ,

    \rm\implies f(343)= log_{\sqrt7} ( 343)

    We can write , 343 as 7³ ,

    \rm\implies f(343)= log_{\sqrt7}7^3

    \rm\implies f(343)=  log_{7^{\frac{1}{2}}} 7^3

    This can be written as ,

    \rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}}

    \rm\implies \boxed{\blue{\rm f(343)= 6 }}

    Hence the required answer is 6.

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