Question:
The value of $\frac{\log_{3} 5 \times \log_{25} 27 \times \log_{49} 7}{\log_{81} 3}$ is
The value of $\frac{\log_{3} 5 \times \log_{25} 27 \times \log_{49} 7}{\log_{81} 3}$ is
Updated On: Apr 27, 2024
- 1
- 6
- $\frac{2}{3}$
- 3
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The Correct Option is D
Solution and Explanation
$\frac{\left(\frac{\log 5}{\log 3} \times \frac{3 \log 3}{2 \log 5} \times \frac{\log 7}{2 \log 7}\right)}{\left(\frac{\log 3}{4 \log 3}\right)} $
$=3\left[\because \log _{a} b=\frac{\log b}{\log a}\right]$
$=3\left[\because \log _{a} b=\frac{\log b}{\log a}\right]$
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Concepts Used:
Limits of Trigonometric Functions
Assume a is any number in the general domain of the corresponding trigonometric function, then we can explain the following limits.
We know that the graphs of the functions y = sin x and y = cos x detain distinct values between -1 and 1 as represented in the above figure. Thus, the function is swinging between the values, so it will be impossible for us to obtain the limit of y = sin x and y = cos x as x tends to ±∞. Hence, the limits of all six trigonometric functions when x tends to ±∞ are tabulated below:
