Understanding Logarithms and Exponential Equations

The video tutorial explains how to evaluate common logarithms by setting up log equations and converting them into exponential equations to solve for x. It covers examples involving large numbers, cube roots, and small numbers, demonstrating the use of negative exponents. The tutorial also shows how to verify calculations using a graphing calculator.

What is the base of a common logarithm?

• Base 5

• Base e

• Base 10

• Base 2

How do you convert a logarithmic equation to an exponential equation?

• By multiplying by the base

• By using the base as the exponent

• By adding the base to both sides

• By squaring both sides

What is the value of x in the equation log base 10 of 110,000 = x?

• 5

• 4

• -5

• -4

How can the cube root of 10 be expressed using a rational exponent?

• 10^2

• 10^1/2

• 10^3

• 10^1/3

What is the value of x in the equation log base 10 of the cube root of 10 = x?

• 1/2

• 3/2

• 1/3

• 2/3

How can 0.001 be expressed as a power of 10?

• 10^3

• 10^-3

• 10^2

• 10^-2

What is the value of x in the equation log base 10 of 0.001 = x?

• 2

• -2

• -3

• 3

Which tool can be used to verify the solutions of logarithmic expressions?

• Scientific calculator

• Graphing calculator

• Slide rule

• Abacus

What is the result of the common log of 110,000?

• -4

• 5

• 4

• -5

What is the result of the common log of 0.1?

• -1

• 1

• -3

• 3