If frac{1}{log_3 pi} + frac{1}{log_4 pi} x, | vedclass

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

Question

(A) Given the inequality: $\frac{1}{\log_3 \pi} + \frac{1}{\log_4 \pi} > x$Using the property $\frac{1}{\log_a b} = \log_b a$,we get:$\log_{\pi} 3 + \

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Given the inequality: $\frac{1}{\log_3 \pi} + \frac{1}{\log_4 \pi} > x$Using the property $\frac{1}{\log_a b} = \log_b a$,we get:$\log_{\pi} 3 + \log_{\pi} 4 > x$Using the property $\log_b m + \log_b n = \log_b (mn)$,we get:$\log_{\pi} (3 	imes 4) > x$$\log_{\pi} 12 > x$We know that $\pi \approx 3.14$,so $\pi^2 \approx 9.86$ and $\pi^3 \approx 31.00$.Since $9.86 Taking $\log_{\pi}$ on all sides:$\log_{\pi} (\pi^2) $2 Since $\log_{\pi} 12 > x$ and $\log_{\pi} 12 > 2$,the value of $x$ can be $2$.

If $\frac{1}{\log_3 \pi} + \frac{1}{\log_4 \pi} > x$,then $x$ can be:

Similar Questions

If $\log _2 x + \log _4 x + \log _8 x + \log _{16} x = \frac{25}{36}$ and $x = 2^k$,then $k$ is

If $x = \log _2 \left( \sqrt {56 + \sqrt {56 + \sqrt {56 + \dots + \infty } } } \right)$,then:

If the sum of the first $20$ terms of the series $\log _{7^{1/2}} x + \log _{7^{1/3}} x + \log _{7^{1/4}} x + \dots$ is $460$,then $x$ is equal to:

If $x$ is a positive real number different from $1$ such that $\log _{a} x, \log _{b} x, \log _{c} x$ are in $AP$,then

For a given number $\alpha > 1$,which of the following is the correct ascending order?

Vedclass Test Series

Exam Paper Generator

Online Exam Module