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.

What is the main goal when evaluating log base 36 of 216?

• To find the logarithm of 216 in base 10

• To calculate the square root of 216

• To find the base that equals 216

• To determine the power to which 36 must be raised to equal 216

Why are whole number exponents not suitable for solving log base 36 of 216?

• They require a calculator

• They do not exist for this problem

• They are too complex to calculate

• They result in numbers too small or too large

What is the purpose of rewriting numbers with the same base when solving logarithmic problems?

• To avoid using a calculator

• To change the base of the logarithm

• To simplify calculations

• To make the numbers larger

Which base allows 36 and 216 to be rewritten for solving the logarithm problem?

• Base 6

• Base 3

• Base 2

• Base 4

What is the final solution for the power to which 36 must be raised to equal 216?

• 5/2

• 1/2

• 2/3

• 3/2