Expanding and Condensing Logarithms Mastery

This video tutorial covers the properties of logarithms, including product, quotient, and power properties. It explains the relationship between exponents and logarithms, providing examples to illustrate these concepts. The tutorial includes practice problems to help students understand how to simplify and expand logarithmic expressions. The lesson concludes with a brief introduction to the next topic, the change of base formula.

What is the relationship between exponents and logarithms?

• They are inversely related.

• They are the same thing.

• They are directly proportional.

• They are unrelated.

When multiplying like bases, what do you do with the exponents?

• Multiply them

• Divide them

• Add them

• Subtract them

What does the product property of logarithms state?

• Log of a quotient equals subtraction of logs

• Log of a product equals sum of logs

• None of the above

• Log of a power equals exponent times log

How do you simplify log base 4 of 16 using the power property?

• Log base 4 of 2

• Log base 4 of 4

• 2

• 4

What property is used to simplify log base 2 of X to the sixth times Y to the fifth?

• Power property

• Product property

• Quotient property

• None of the above

When expanding logarithms, what does division turn into?

• Multiplication

• Addition

• Subtraction

• No change

What is the result of applying the power property to log base 9 of X to the 4th?

• X log base 9 of 4

• None of the above

• Log base 9 of 4X

• 4 log base 9 of X

How can 125 be rewritten using exponents?

• 2 to the power of 5

• 25 to the power of 2

• 3 to the power of 5

• 5 to the power of 3

In the expression log base 3 of 250 minus log base 3 of 37, what property is primarily used?

• Product property

• Quotient property

• Power property

• None of the above

What does log base 3 of 9 simplify to?

• 3

• 9

• 2

• 1