If $ 3^x = 4^{ x - 1} $ then x is equal to
- $ \frac{ 2 \, log_3 \, 2}{ 2 log_3 2 - 1}$
- $ \frac{ 2}{ 2 log_2 3 }$
- $ \frac{ 1}{ 1 - log_4 3 } $
- $ \frac{ 2 log_2 \, 3} { 2 log_2 3 - 1}$
The Correct Option is C
Solution and Explanation
Top Questions on Exponential and Logarithmic Functions
- Find the value of \( \log_3 81 \).
- MHT CET - 2025
- Mathematics
- Exponential and Logarithmic Functions
- Solve for \( x \): \( \log_2 (x-1) = 3 \).
- MHT CET - 2025
- Mathematics
- Exponential and Logarithmic Functions
- If \( \log_2 3 = p \), express \( \log_8 9 \) in terms of \( p \):
- AP EAPCET - 2025
- Mathematics
- Exponential and Logarithmic Functions
- If $f : \mathbb{R}^+ \to \mathbb{R}$ is defined as $f(x) = \log_a x$ where $a>0$ and $a \neq 1$, prove that $f$ is a bijection. (R$^+$ is the set of all positive real numbers.)
- CBSE CLASS XII - 2025
- Mathematics
- Exponential and Logarithmic Functions
- \( \int \sin^{-1}\left(\frac{x}{\sqrt{a+x}}\right) \, dx = \)
- AP EAPCET - 2025
- Mathematics
- Exponential and Logarithmic Functions
Questions Asked in JEE Advanced exam
- Consider a star of mass $ m_2 $ kg revolving in a circular orbit around another star of mass $ m_1 $ kg with $ m_1 \gg m_2 $. The heavier star slowly acquires mass from the lighter star at a constant rate of $ \gamma $ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is $ r $, then its relative rate of change $ \frac{1}{r} \frac{dr}{dt} $ (in s$^{-1}$) is given by:
- JEE Advanced - 2025
- Gravitation
- A projectile is thrown at an angle of \(60^\circ\) with the horizontal. Initial speed is \(270\, \text{m/s}\). A linear drag force \(F = -CV\) acts on the body. Find the horizontal displacement till \(t = 2\) seconds. Given \(C = 0.1\, \text{s}^{-1}\).
- JEE Advanced - 2025
- Projectile motion
The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____.
Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80- JEE Advanced - 2025
- Organic Chemistry
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is
- JEE Advanced - 2025
- Coordinate Geometry
As shown in the figures, a uniform rod $ OO' $ of length $ l $ is hinged at the point $ O $ and held in place vertically between two walls using two massless springs of the same spring constant. The springs are connected at the midpoint and at the top-end $ (O') $ of the rod, as shown in Fig. 1, and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $ f_1 $. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2, and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $ f_2 $. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{f_1}{f_2}$ is:
- JEE Advanced - 2025
- Waves and Oscillations
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)