List of top Mathematics Questions on Exponential and Logarithmic Functions

The range of the function $f(x)=\left(\frac{1}{3}\right)^{3+\sin x}$ is

If \(\log_8 x = \frac{1}{3}\), find the value of \(x\).

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

Find the function \( f \) which satisfies the equation \( \frac{df}{dx} = 2f \), given that \( f(0) = e^3 \)

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.)

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
\[ 1 + \frac{\log x}{1!} + \frac{(\log x)^2}{2!} + \cdots = \]

The solution of \( 3^{2x-1} = 81^{1-x} \) is:

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax + b^2 = 0 \), then \( \alpha^2 + \beta^2 \) is equal to:

The value of \( x \) such that \( 3^{2x} - 2(3^{x+2}) + 81 = 0 \) is:

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax + b^2 = 0 \), then \( \alpha^2 + \beta^2 \) is equal to:

The value of \( x \) such that \( 3^{2x} - 2(3^{x+2}) + 81 = 0 \) is:

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax + b^2 = 0 \), then \( \alpha^2 + \beta^2 \) is equal to:

The value of \( x \) such that \( 3^{2x} - 2(3^{x+2}) + 81 = 0 \) is:

For 8^2x - 16.8^x + 48 = 0, the sum of values of x is equal to: