List of top Mathematics Questions on Exponential and Logarithmic Functions

If $\log_a b = 2$, then $b = ?$
Find the value of \( \log_3 81 \).
Solve for \( x \): \( \log_2 (x-1) = 3 \).
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.)
Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).
If \( \log_2 x = 5 \), what is the value of \( x \)?
Find the value of \( \log_2 32 \).
The sum of all the solutions of the equation \[(8)^{2x} - 16 \cdot (8)^x + 48 = 0\]is:
The sum of all the real roots of the equation \((e^{2x} – 4)(6e^{2x} – 5e^x + 1) = 0\) is
If \(x > 0\), then
\[ 1 + \frac{\log x}{1!} + \frac{(\log x)^2}{2!} + \cdots = \]
For 82x - 16.8x + 48 = 0, the sum of values of x is equal to: