Question is self-explanatory.

Solve y in terms of x from the equation \(\frac{49^{x+4}}{7^{y-5}}\)\( = 2401\).

Solve the indefinite integral \( \int \frac{3x^{4} - 4}{2x^{3}}\)\(dx\).

Question is self-explanatory.

Solve: \(\;\) \(2\log_{2}(x - 3) - \log_{2}(6-x) = 2\).

Solve the given equations for x and y: \(5x + 3y = 10 \) and \(-x + y = -10 \).

Problem: \(\sin(x) + \cos(x) = 3/2 \; \Rightarrow \) To find: \(\tan(x)\).

Evaluate \(\sqrt{54^3+72^3+90^3}\).

Problem: \(x^2 - x^3 ={\Large\frac{5}{216}}\), find \(x\).

To evaluate: \(\sqrt{i}+\sqrt{-i}\).

Alternative method of solving problem from Post 10. To evaluate: \(\sqrt{i}+\sqrt{-i}\).

Evaluate \(\sqrt{81^6-81^5}\).

False ambiguity in solving problem from Post 10 and Post 11. To evaluate: \(\sqrt{i}+\sqrt{-i}\).

Polar form solution to solve problem from Post 10. To evaluate: \(\sqrt{i}+\sqrt{-i}\).

Evaluate \(\sqrt{21^7-21^6}\) without a calculator.

\(\sqrt{a} + \sqrt{b} = 10 \) and \(\sqrt{ab} = 10 \). Find a & b.

If \(S = \sum_{i=0}^{N} x^i \) prove: 1) \(xS = \sum_{i=1}^{N+1} x^i \), 2) \(S - xS = 1 - x^{N+1} \), and, 3) \(S = (1 - x^{N+1})/(1 - x) \)

Prove \(x=\Large\frac{-b\pm\sqrt{b^2-4ac}}{2a} \)