Logarithmic and Exponential Equations

Mr. Garrett explains how to solve exponential and logarithmic equations using various methods. He covers equating exponents, using logarithms, and converting to exponential form. The video includes examples and emphasizes checking for extraneous solutions. The tutorial aims to equip students with the skills to choose appropriate methods for different equations.

What is the first step in solving exponential and logarithmic equations?

• Guess the solution.

• Use a calculator.

• Identify the type of equation.

• Choose a random method.

When equating exponents, what must be true about the bases?

• They must be different.

• They must be the same.

• They must be even numbers.

• They must be prime numbers.

How can you express 64 as a power of 4?

• 4^5

• 4^4

• 4^3

• 4^2

What is the solution to the equation 4^x = 64?

• x = 2

• x = 3

• x = 4

• x = 5

What is the base of 100 when expressed as a power of 10?

• 10^4

• 10^3

• 10^2

• 10^1

In the equation 100^(7x+1) = 1000^(3x-2), what is the base of 1000?

• 10^3

• 10^1

• 10^4

• 10^2

What is the solution to the equation 10^(14x+2) = 10^(9x-6)?

• x = -5/8

• x = 5/8

• x = 8/5

• x = -8/5

When bases cannot be equated, what method is used to solve exponential equations?

• Elimination

• Graphing

• Taking logarithms

• Substitution

What is the approximate value of log base 4 of 11?

• 1.7297

• 1.9727

• 1.2977

• 1.9277

What is the exact value of x in the equation 7^(9x) = 15?

• log base 9 of 7 divided by 15

• log base 9 of 15 divided by 7

• log base 7 of 15 divided by 9

• log base 15 of 7 divided by 9