True or False: Logarithms can only be used for whole numbers.

False; logarithms can be applied to any positive real numbers.

Riddle: I am a mathematical operation that transforms multiplication into addition. What am I?

Logarithm

When multiplying 16 by 8 using powers, what is the new power obtained from adding the indices?

7; since 16 = 2⁴ and 8 = 2³, then 16 × 8 = 2⁴ × 2³ = 2⁷.

What does the expression log₂16 = 4 represent in terms of powers?

It represents that 2 raised to the power of 4 equals 16.

i.e.,

2⁴ = 16

Fill in the blank: The logarithmic form of the statement 64 = 8² is ___ = 2.

Log₈64

True or False: The statement log₃27 = 3 implies that 3³ = 27.

True

The first law of logarithms states that log_a(xy) = ___ + ___.

log_a x + log_a y

What does the second law of logarithms state when evaluating log_a(x^m)?

What is the third law of logarithms when dividing two numbers in logarithmic form?

The third law states that logₐ(x/y) = logₐ(x) - logₐ(y), which expresses the logarithm of a quotient as the difference of the logarithms.

The logarithm of 1 in any base is ___.

Riddle: I am a number that represents a power of 2, and when asked what I am, my answer is 3. What logarithm am I?

Log₂(8), because 8 = 2³.

The logarithm to base e is also known as ___ logarithm.

Natural logarithm

True or False: Logarithms to base 10 can be calculated using the button marked 'log' on a standard calculator.

True

I am a constant approximately equal to 2.718, commonly used in logarithmic functions. What am I?

e (the exponential constant)

The logarithm function is the inverse of which mathematical operation?

The logarithm function is the inverse of exponentiation.

True or False: The logarithm of a number less than 1 is always positive.

False. The logarithm of a number less than 1 is always negative.