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 first step in evaluating log base 2 of 1/8 without a calculator?

• Convert the logarithm to a fraction

• Rewrite the logarithm as an exponential equation

• Change the base of the logarithm

• Use a calculator to find the value

How can 1/8 be expressed using a base of 2?

• 2^8

• 2^1/3

• 2^-3

• 2^3

What property of exponents is used to rewrite 8 as a base of 2?

• Negative exponent property

• Power of a power property

• Quotient of powers property

• Product of powers property

Once the bases are the same, what is the next step in solving the equation?

• Divide the exponents

• Set the exponents equal to each other

• Multiply the exponents

• Add the exponents

What is the solution to the equation 2^x = 1/8?

• x = -3

• x = 3

• x = -1/3

• x = 1/3