Tutorial - Evaluating Logarithms Without a Calculator

The video tutorial explores solving logarithmic problems without a calculator. It begins with an introduction to logarithms and sets up a problem involving log base 36 of 216. The teacher examines different powers of 36, including negative powers, to find a solution. The tutorial then explores using fractions and properties of exponents to solve the problem. The teacher identifies a common base for 36 and 216, rewriting them as powers of 6. Finally, the solution is explained using the one-to-one property of exponents, concluding that the answer is three halves.

How can you express 36 in terms of base 6, and what is the significance of this expression?

What is the final value of x when solving the equation 2^x = 6^3, and how did you arrive at this conclusion?