Expanding and Condensing Logarithms: Key Concepts and Examples

What operation does expanding logarithms resemble when multiplying?

• Addition

• None of the above

• Subtraction

• Division

When dividing logarithms, what operation do we use between the logs?

• None of the above

• Addition

• Subtraction

• Multiplication

How do you handle a logarithm of a power when expanding?

• Subtract the exponent from the log

• Add the exponent to the log

• Divide the log by the exponent

• Multiply the log by the exponent

In the example of expanding log base 4 of x^2 * y^3, what is the first step?

• Separate the multiplication into the sum of logs

• Combine the logs into one

• Bring the exponents down in front of the logs

• Convert the base of the logarithms

What is the result of condensing log base 9 of X plus log base 9 of Y minus log base 9 of Z?

• log base 9 of (X*Y)/Z

• log base 9 of X/Y-Z

• log base 9 of X+Y-Z

• log base 9 of X*Y*Z

When condensing, what do you do with coefficients in front of the logs?

• Add them to the base

• Ignore them

• Divide the log by the coefficients

• Convert them into exponents

In the process of condensing, how do you handle addition and subtraction between logs?

• Convert addition into multiplication of arguments

• Convert subtraction into division of arguments

• None of the above

• Both A and B are correct

What is the final step in condensing log base e of x^4 divided by y^5 * z^6?

• Combine all logs into one

• Separate each term into its own log

• Multiply the arguments

• Divide the arguments

How do you handle a square root when condensing logarithms?

• Treat it as a 1/2 exponent

• Add 1/2 to the base of the log

• Multiply the log by 1/2

• Ignore the square root

What does the cube root transform into when condensing a logarithm?

• A 1/3 exponent

• A multiplication by 1/3

• It is ignored

• A division by 3