Exploring Logarithms and Their Graphs

What is the relationship between exponentials and logarithms?

• Logarithms are the square roots of exponentials.

• Logarithms and exponentials are inversely related.

• Logarithms are the derivatives of exponentials.

• There is no relationship between logarithms and exponentials.

Why can't the argument of a logarithm be zero or negative?

• Because logarithms only work with positive numbers.

• Because the base of a logarithm cannot be negative.

• Because you cannot take the logarithm of zero or a negative number.

• Because the output of a logarithm is always positive.

How do you find the inverse of an exponential function?

• By subtracting the exponent from the base.

• By taking the square root of the base.

• By dividing by the base.

• By reflecting it across the y = x line.

What does a logarithm do to an exponential equation?

• It divides the base by the exponent.

• It multiplies the base and exponent.

• It separates the base from the exponent.

• It adds the base to the exponent.

What is the base of a common logarithm?

• 2

• Any positive number

• 10

• e (Euler's number)

What is the base of a common log if not specified?

• 1

• e

• 2

• 10

What does 'ln' stand for in logarithmic notation?

• Logarithm neutral

• Logarithm notation

• Logarithm natural

• Logarithm number

How can you solve a logarithm using exponential notation?

• By combining the base and exponent

• By multiplying the base and exponent

• By setting the base to zero

• By separating the base from the exponent

What must the argument of a logarithm be for it to be defined?

• Zero

• Positive

• Negative

• Any real number

What is the result of any logarithm where the argument is 1?

• 1

• The base of the logarithm

• 0

• Undefined