Only 10% Students Solve this exponential math olympiad question | 2^t =t^32 |

Summary

This video provides a step-by-step solution to an interesting exponential math Olympiad problem: 2^t = t^32, where the goal is to find the value of 't'. The presenter uses exponential rules and algebraic manipulation to arrive at the solution.

Highlights

Introduction to the Problem00:00:00

The video introduces an exponential math Olympiad question: 2^t = t^32, and aims to solve for 't' using an easy method.

Applying Exponent 1/t to Both Sides00:00:35

The first step involves raising both sides of the equation to the power of 1/t. Using the exponential formula (a^n)^m = a^(nm), the equation transforms to 2 = t^(32/t).

Applying Exponent 1/32 to Both Sides00:01:43

Next, the presenter applies the exponent 1/32 to both sides of the equation. After simplification, the equation becomes 2^(1/32) = t^(1/t).

Manipulating the Left Side to Match the Right Side Form00:02:30

To solve for 't', the presenter begins to manipulate the left side of the equation (2^(1/32)) to match the form of the right side (t^(1/t)). This is done by multiplying the exponent by '2/2', resulting in (2^2)^(1/(2*32)) which simplifies to 4^(1/64).

Further Manipulation for a Match00:03:46

The process is repeated. The left side (4^(1/64)) is further manipulated by multiplying the exponent by '2/2', leading to (4^2)^(1/(2*64)), which simplifies to 16^(1/128).

Verification of the Solution00:05:22

The solution t = 256 is verified by substituting it back into the original equation 2^t = t^32. Both sides simplify to 2^256, confirming the correctness of the answer. The video concludes by thanking viewers.

Final Manipulation and Solution00:04:30

The manipulation is done one more time with 16^(1/128). Multiplying the exponent by '2/2' gives (16^2)^(1/(2*128)), which simplifies to 256^(1/256). By comparing this with t^(1/t), it is evident that t = 256.