Evaluating a Logarithm To a Fraction Without a Calculator

The video tutorial explains how to evaluate the expression log base 2 of 1/8 without using a calculator. The instructor begins by rewriting the expression in exponential form, setting it equal to X. The goal is to find the power to which 2 must be raised to equal 1/8. The instructor demonstrates how to rewrite the expression so that both sides have the same base, using properties of exponents. By equating the exponents, the solution is found to be -3.

What is the significance of having the same base when solving exponential equations?

How do you determine the value of X when the bases are the same in an exponential equation?