Logarithmic Properties and Expressions

The video tutorial explains how to write logarithmic expressions as a single logarithm. It covers converting constants into logarithmic form using base 10 and base 4, applying the power property, and combining logarithms using the quotient property. The tutorial provides step-by-step instructions and examples to help understand these concepts.

What is the base of the common logarithm used in the expression 2 - log x?

• Base 10

• Base e

• Base 2

• Base 5

How can the number 2 be expressed as a logarithm with base 10?

• log base 10 of 10

• log base 10 of 20

• log base 10 of 2

• log base 10 of 100

What property of logarithms allows the coefficient to be moved to the exponent position?

• Change of Base Property

• Quotient Property

• Product Property

• Power Property

What is the result of combining log base 10 of 100 and log base 10 of x using the quotient property?

• log base 10 of 10

• log base 10 of x/100

• log base 10 of 100/x

• log base 10 of 100x

In the expression 1/2 + 2 log base 4 of 5, what is the base of the logarithms?

• Base 2

• Base 10

• Base 4

• Base 5

How is 1/2 expressed as a logarithm with base 4?

• log base 4 of 1

• log base 4 of 2

• log base 4 of 4

• log base 4 of 8

What is the result of applying the power property to 2 log base 4 of 5?

• log base 4 of 5

• log base 4 of 50

• log base 4 of 10

• log base 4 of 25

What is the final simplified form of the expression 1/2 + 2 log base 4 of 5?

• log base 4 of 10

• log base 4 of 100

• log base 4 of 25

• log base 4 of 50

Which property of logarithms is used to combine log base 4 of 2 and log base 4 of 25?

• Change of Base Property

• Power Property

• Product Property

• Quotient Property

What is the value of 4 raised to the power of 1/2?

• 1

• 2

• 3

• 4