The real part of $log \,log\, i$ is
- $ \frac{\pi}{2}$
- $\log \frac{\pi}{2}$
- $0$
- $none\, of\, these$
The Correct Option is B
Solution and Explanation
Top Questions on 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
If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
- TS EAMCET - 2023
- 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
- If \(y =\)\(e^{\sqrt{x\sqrt{x\sqrt{x\ldots}}}}\) \(x>1,\) then \(\left. \frac{{d^2y}}{{dx^2}} \right|_{x = \log_e 3}\) is
- KCET - 2022
- Mathematics
- Exponential and Logarithmic Functions
Questions Asked in COMEDK exam
- The standard electrode potential for Daniell cell is $1.1\, volt$. What is the standard Gibbs energy for the reaction?
- COMEDK - 2015
- Gibbs Free Energy
- The girth or diameter of the stem increases due to the activity of the following
- COMEDK - 2015
- The Stem
- More number of oxidation state are exhibited by the actinoids than by lanthanoids. The main reason for this is :
- COMEDK - 2015
- The Actinoids
- Two amplifiers are connected one after the other in series (cascaded). The first amplifier has a voltage gain of $10$ and the second has a voltage gain of $20$. If the input signal is $0.01\, volt$, what is the output $ac$ signal ?
- COMEDK - 2014
- Transistors
- Three charges $-q, +Q$ and $-q$ are placed at equal distances along a straight line. If the total $P.E.$ of the system is zero, the ratio $ \frac{Q}{q} $ becomes
- COMEDK - 2014
- Electrostatic potential
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)