Solving Exponential Equations: Logarithms Explained

The video tutorial introduces the importance of understanding logs as a learning goal. It explains the three types of logs: regular, common, and natural, and their applications in solving exponential functions. The tutorial provides a step-by-step guide on using logs to solve equations, including example problems and detailed solutions. Students are reminded to take the video seriously as it will be graded, and they are encouraged to practice independently.

Why is it important to take the video and questions seriously?

• Because it will be graded as a learning goal

• Because it is just for fun

• Because it is optional

• Because it will not affect your grade

What is the base of a common logarithm?

• Any number

• 10

• e

• 2

What is the base of a natural logarithm?

• 2

• e

• Any number

• 10

When solving exponential functions, what should you do if the base is 10?

• Multiply both sides by 10

• Take the log of both sides

• Divide both sides by 10

• Take the natural log of both sides

What should you do if the base of the exponential function is e?

• Divide both sides by e

• Multiply both sides by e

• Take the log of both sides

• Take the natural log of both sides

What is the first step in solving the equation 5^(9x-3) = 51?

• Take the log of both sides

• Divide by 5

• Multiply by 5

• Add 3 to both sides

In the equation e^(4m+1.3) = 9, what type of log should be used?

• Any log

• Natural log

• Common log

• Base 2 log

What does the power rule state?

• Divide the exponent by the base

• Multiply the exponent by the base

• Drop the exponent to the front

• Add the exponent to the base

What is the next step after applying the power rule in the equation 9x - 3 = log(51)/log(5)?

• Divide by 9

• Multiply by 9

• Subtract 3 from both sides

• Add 3 to both sides

What is the final value of x in the equation 9x - 3 = log(51)/log(5)?

• 0.605

• 5.44

• 2.44

• 0.224