Logarithmic Concepts and Properties

The video tutorial explains how to solve exponential equations using logarithms. It covers two examples: one using natural logarithms and the other using common logarithms. The process involves isolating the exponential part, applying the power property of logarithms, and verifying the solution. The tutorial emphasizes the use of calculators for accurate results and demonstrates the verification of solutions by checking the approximations.

What is the first step in solving an exponential equation using logarithms?

• Add a constant to both sides

• Subtract the base from both sides

• Multiply both sides by the base

• Isolate the exponential part

Why can't seventy-eight be expressed as five raised to some power in the first example?

• Because seventy-eight is a prime number

• Because seventy-eight is not a power of five

• Because seventy-eight is an even number

• Because five is not a factor of seventy-eight

What property of logarithms is used to bring the exponent down in the first example?

• Power property

• Product property

• Change of base property

• Quotient property

After applying the power property of logarithms, what is the next step to solve for x in the first example?

• Subtract the natural log of five from both sides

• Add the natural log of five to both sides

• Divide both sides by the natural log of five

• Multiply both sides by the natural log of five

What is the approximate value of x in the first example after rounding?

• 3.1415

• 2.7070

• 1.6180

• 2.5000

In the second example, why is the common log used instead of the natural log?

• Because the base is a negative number

• Because the base is ten

• Because the base is a prime number

• Because the base is a fraction

What is the value of the common log of ten?

• Zero

• One

• Negative one

• Ten

What is the approximate value of x in the second example after rounding?

• 0.0880

• 0.5000

• 0.3333

• 0.2500

What is the decimal equivalent of two-thirds used for verification in the second example?

• 0.8

• 0.7

• 0.6 repeating

• 0.5

What is the purpose of verifying the solution in both examples?

• To find a new solution

• To ensure the solution is correct

• To change the base of the logarithm

• To simplify the equation further