List of top Mathematics Questions on Exponential and Logarithmic Functions asked in KEAM

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

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: