Question:
If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then
If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then
Updated On: Apr 26, 2024
- $4
- $x\, 4$
- $-1 \le x\le5$
- $x\, 5$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Given, $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$ if and only if
$x^{2}-16 \leq 4 x-11$
$\Rightarrow x^{2}- 4 x-5 \leq 0$
$x^{2}-5 x+x-5 \leq 0$
$\Rightarrow x(x-5)+1(x-5) \leq 0$
$(x-5)(x+1) \leq 0$
Sign scheme of $x^{2}-4 x-5 \leq 0$
Was this answer helpful?
0
1
Top Questions on Exponential and Logarithmic Functions
- The value of \(\log_6 2 + \log_6 3\) is:
- TS POLYCET - 2024
- Mathematics
- Exponential and Logarithmic Functions
- Exponential form of \(\log_b a = c\) is:
- TS POLYCET - 2024
- Mathematics
- Exponential and Logarithmic Functions
- The sum of all the solutions of the equation \[(8)^{2x} - 16 \cdot (8)^x + 48 = 0\]is:
- JEE Main - 2024
- Mathematics
- Exponential and Logarithmic Functions
- Let \(a=3\sqrt2\) and \(b=\frac{1}{5^{1/6}\sqrt5}\). If x, y ∈ R are such that
\(3x+2y=\log_a(18)^{\frac{5}{4}}\) and
\(2x-y=\log_b(\sqrt{1080})\),
then 4x + 5y is equal to _______.- JEE Advanced - 2024
- Mathematics
- Exponential and Logarithmic Functions
- The value of \(\frac{1}{\log_3{60}} + \frac{1}{\log_4{60}} + \frac{1}{\log_5{60}}\) is
- AP POLYCET - 2023
- Mathematics
- Exponential and Logarithmic Functions
View More Questions
Questions Asked in WBJEE exam
- If 1000! = 3n × m, where m is an integer not divisible by 3, then n =?
- WBJEE - 2024
- Probability
- Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is:
- If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by \(l + m + n = 0\), \(2lm + 2mn - ln = 0\), then the angle between the lines is:
- WBJEE - 2024
- Vectors
- If \(a, b, c\) are distinct odd natural numbers, then the number of rational roots of the equation \(ax^2 + bx + c = 0\) is:
- WBJEE - 2024
- Quadratic Equation
- What force \(F\) is required to start moving this 10 kg block shown in the figure if it acts at an angle of \(60^\circ\) as shown? (\(\mu_s = 0.6\)).
- WBJEE - 2024
- laws of motion
View More Questions
Concepts Used:
Exponential and Logarithmic Functions
Logarithmic Functions:
The inverses of exponential functions are the logarithmic functions. The exponential function is y = ax and its inverse is x = ay. The logarithmic function y = logax is derived as the equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, (where, a > 0, and a≠1). In totality, it is called the logarithmic function with base a.
The domain of a logarithmic function is real numbers greater than 0, and the range is real numbers. The graph of y = logax is symmetrical to the graph of y = ax w.r.t. the line y = x. This relationship is true for any of the exponential functions and their inverse.
Exponential Functions:
Exponential functions have the formation as:
f(x)=bx
where,
b = the base
x = the exponent (or power)