List of top Mathematics Questions on Exponential and Logarithmic Functions

If $\log_a b = 2$, then $b = ?$

Evaluate \[ \int \frac{1}{1 + x^2} \, dx = ? \]

Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]

\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}

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.)

Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]

$\int (x^3 y^3) \, dx =$
Identify the correct option from the following:

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 _______.

The sum of all the solutions of the equation \[(8)^{2x} - 16 \cdot (8)^x + 48 = 0\]is:

The value of \(\log_6 2 + \log_6 3\) is:

Exponential form of \(\log_b a = c\) is:

If the graph of the anti derivative \( g(x) \) of \( f(x) = \log(\log x) + (\log x)^{-2} \) passes through \( (e, 2023 - e) \) and the term independent of \( x \) in \( g(x) \) is \( k \), then the sum of all the digits of \( k \) is

The value of $a^{\log_b c} - c^{\log_b a}$, where $a, b, c>0$ but $a, b, c \neq 1$, is