The sum of all the natural numbers for which | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 -

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(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 -

Similar Questions

Find the roots of the equation $2^{x + 2} \cdot 27^{x/(x - 1)} = 9$.

Evaluate the sum: $\sum\limits_{k = 1}^n \frac{1}{\log_{2^k}(a)}$

If $x = \log_3 5$ and $y = \log_{17} 25$,then which of the following is correct?

The solution of $\log_{\sqrt{3}} x + \log_{\sqrt[4]{3}} x + \log_{\sqrt[6]{3}} x + \dots + \log_{\sqrt[16]{3}} x = 36$ is

If $a^x = b^y = c^z = d^w$, the value of $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module