# Let f(x) =1+3^x log 3 and F(x) be its antiderivative which assume the value 7 for x=2 . The value of x for which the curve F(x) cuts the abscissa axis is

Solution:

$F(x)=\int f(x)\hspace{0.1cm}dx+C=x+3^{x}+C$  but $F(2)=7$

$\Rightarrow$       $7=2+9+C$

$\Rightarrow$      $C=-4$  .Hence  $F(x)=x+3^{x}-4.$ Now  $F(x)=0$

$\Rightarrow$       $x=1.$

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