The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 6x + 5 = 0\), evaluate \(\frac{\beta}{\alpha} + \frac{\alpha}{\beta}\).

Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\).

Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.

Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.

If \(f(x) = x^{2}\) and \(g(x) = \sin x\), find g o f.

Solve: \(\sin \theta = \tan \theta\)

A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the invers...

If \(\sqrt{x} + \sqrt{x + 1} = \sqrt{2x + 1}\), find the possible values of x.