The sum of all the natural numbers for which | vedclass

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(C) For the logarithm $\log_{b}(a)$ to be defined,we must have $a > 0$,$b > 0$,and $b 
eq 1$.$1$. For the argument: $x^2 - 14x + 45 > 0$$(x - 5)(x -

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$3$

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(C) For the logarithm $\log_{b}(a)$ to be defined,we must have $a > 0$,$b > 0$,and $b 
eq 1$.$1$. For the argument: $x^2 - 14x + 45 > 0$$(x - 5)(x - 9) > 0$$x \in (-\infty, 5) \cup (9, \infty) \dots (1)$$2$. For the base: $4 - x > 0$ and $4 - x 
eq 1$$x $3$. Intersection of $(1)$ and $(2)$:$x \in (-\infty, 3) \cup (3, 4)$Since we are looking for natural numbers $(x \in \{1, 2, 3, \dots\})$,the values of $x$ that satisfy the condition are $x = 1$ and $x = 2$.The sum of these natural numbers is $1 + 2 = 3$.

The sum of all the natural numbers for which $\log_{(4-x)}(x^2 - 14x + 45)$ is defined is -

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