Question

If f(x)=3^1+logx÷x^log3 , then f(2005)=
(a) log 2005
(b) (2005)log 3
(c) 1/2005
(d) 3​

Answer 1

Step-by-step explanation:

Here is your answer hope it helps you

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf If \: f(x) = \frac{ {3}^{1 + log x} }{ {x}^{log 3} } \: \: then \: f(2005)$

(a) log 2005

(b) (2005)log 3

$\displaystyle \sf (c) \: \: \frac{1}{2005}$

(d) 3

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\displaystyle \sf {3}^{log x} = {x}^{log 3}$

EVALUATION

Here the given function is

$\displaystyle \sf f(x) = \frac{ {3}^{1 + log x} }{ {x}^{log 3} }$

$\displaystyle \sf \implies \: f(x) = \frac{ {3}^{1} . {3}^{ log x} }{ {x}^{log 3} }$

$\displaystyle \sf \implies \: f(x) = \frac{ 3 \times {3}^{ log x} }{ {3}^{ log x} }$

$\displaystyle \sf \implies \: f(x) = 3$

Putting x = 2005 we get

$\displaystyle \sf f(2005) = 3$

FINAL ANSWER

Hence the correct option is (d) 3

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