Logic Stories

Post #001 Solve: w2 - w3 = 12

Question is self-explanatory.

Post #002 Solve y in Terms of x from an Exponential Equation

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

Post #003 Finding the Indefinite Integral

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

Post #004 Factorizing 12x2 + 25x − 22.

Question is self-explanatory.

Post #005 Solving a Logarithmic Equation

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

Post #006 Solving a Linear System Using Substitution

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

Post #007 Solving Tangent from a Sin-Cos Sum

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

Post #008 Evaluating the Square Root of the Sum of Three Cubes

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

Post #009 Solving a Cubic-Quadratic Difference

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

Post #010 Sum of Root i and Root -i: Solution 1

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