Understanding Logarithmic Properties

What does the product property of logarithms state?

• The log of a product is the quotient of the logs.

• The log of a product is the product of the logs.

• The log of a product is the difference of the logs.

• The log of a product is the sum of the logs.

How do you apply the quotient property to log base B of X divided by Y?

• log base B of X / log base B of Y

• log base B of X * log base B of Y

• log base B of X + log base B of Y

• log base B of X - log base B of Y

When expanding log base 2 of 5x squared Y divided by 3, what property allows you to bring the exponent down in front of the log?

• Quotient property

• Product property

• Power property

• Base property

In the example of log base 4 of X divided by WYZ, why do we subtract the logs of W, Y, and Z?

• Because they are in the denominator and multiplied together.

• Because they are in the numerator and added together.

• Because they are in the numerator and multiplied together.

• Because they are in the denominator and added together.

What does the power property of logarithms allow you to do with the exponent?

• Raise the base of the log to the power of the exponent.

• Bring it down in front of the log as a coefficient.

• Divide it by the base of the log.

• Multiply it by the base of the log.

When condensing logs, what operation corresponds to adding logs?

• Multiplication

• Subtraction

• Division

• Exponentiation

In the condensing example with common logs, why do we bring coefficients up as powers?

• To simplify the expression.

• To apply the quotient property in reverse.

• To apply the product property in reverse.

• To apply the power property in reverse.

What is the base of a natural log (Ln)?

• 10

• 2

• e (approximately 2.71)

• π (Pi)

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How do you handle negative signs when condensing logs with subtraction?

• By adding the logs together.

• By taking the reciprocal of the base.

• By distributing the negative sign to each log.

• By converting them into positive signs.

What does condensing logarithms involve?

• Splitting a single log into multiple logs.

• Applying the power property to each log.

• Combining multiple logs into a single log.

• Changing the base of the logarithms.