Logarithmic Functions and Properties

This video tutorial introduces common logarithms, focusing on base 10 logarithms and their applications. It explains how to evaluate logarithms using calculators and solve exponential equations that lack a common base. The tutorial also covers advanced logarithmic problems, demonstrating algebraic methods to solve them. Additionally, it discusses graphing logarithmic functions and using calculators for complex equations.

What is the base of common logarithms?

• Base 2

• Base 10

• Base e

• Base 5

Why are base 10 logarithms significant in calculators?

• They are easier to compute manually.

• They are used for graphing functions.

• They are pre-programmed in calculators.

• They are the only logarithms used in mathematics.

How do you evaluate log(100) using a calculator?

• Enter log(100) and close the bracket.

• Enter log(100) without closing the bracket.

• Enter log(100) and divide by 10.

• Enter log(10) and multiply by 2.

What is the result of log(537) to the nearest tenth?

• 3.2

• 2.5

• 3.0

• 2.7

How do you solve 3^x = 20 using logarithms?

• Find a common base for 3 and 20.

• Use the power law to isolate x.

• Divide both sides by 3.

• Multiply both sides by 20.

What is the purpose of the power law in logarithms?

• To divide exponents.

• To multiply exponents.

• To bring the exponent to the front.

• To add exponents together.

In the equation 4^(x+1) = 9, what is the first step to solve it using logarithms?

• Subtract 1 from both sides.

• Multiply both sides by 9.

• Take the log of both sides.

• Divide both sides by 4.

Why is it important to use brackets when applying the power law to a binomial exponent?

• To ensure the entire exponent is multiplied.

• To simplify the equation.

• To avoid division errors.

• To make the equation look neat.

What is the advantage of using the algebraic method for complex logarithmic equations?

• It works better for complicated questions.

• It requires less algebra.

• It is faster for simple equations.

• It avoids the use of calculators.

In the equation 5 * 3^x = 10^(x+1), what is the first step to solve it using logarithms?

• Take the log of both sides.

• Subtract x from both sides.

• Multiply both sides by 5.

• Divide both sides by 10.