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RARE & TOUGH COMPLEX LOGARITHMIC FUNCTIONS PROBLEM SOLVED HERE.

Do you want to know the solution for Challenging Advanced Complex Functions Problem:x^(ln y) + y^(ln x) = (ln x)^y + (ln y)^x in IIT JEE maths Functions? You are at the right place.

Solving a Rare & Tough Complex Functions Problem — Exclusively by an IITian!

In this video, we solve a highly challenging equation that appears in advanced math circles:

x^(ln y) + y^(ln x) = (ln x)^y + (ln y)^x

We assume x and y are complex conjugates on the unit circle:
x = e^(iθ), y = e^(-iθ), with x ≠ y and x, y ≠ 0, 1.

Using the principal branch of the complex logarithm, Euler’s formula, and properties of complex exponentiation, we simplify both sides and reduce the problem to a single equation in θ.

After analytical simplification and numerical solving, we find a precise solution:

θ ≈ 1.068 radians

This problem sits at the intersection of JEE Advanced-level ingenuity and CSIR-NET Mathematics depth. It’s not found in standard textbooks—it tests true conceptual mastery of complex functions, logarithmic branches, and symmetry.

Learn advanced complex functions in this IIT JEE Maths video. Solve rare logarithmic functions and delve into complex analysis with Euler formula.

Perfect for:
• JEE Advanced aspirants targeting top ranks
• CSIR-NET / UGC-NET Mathematics candidates
• Math Olympiad enthusiasts
• Anyone who loves deep, elegant problem-solving

You’ll learn:
✓ How to handle complex exponentiation correctly
✓ Why x^(ln y) = y^(ln x) in the complex plane (under proper branches)
✓ How to reduce a two-variable complex equation to one real parameter
✓ How to verify transcendental solutions numerically with confidence

This is more than a solution—it’s a masterclass in mathematical thinking by an IIT graduate.

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