How To Evaluate a Logarithm When the Answer is a Negative Exponent

The video tutorial explains how to evaluate a logarithmic expression by converting it into exponential form. It discusses the properties of logarithms, particularly focusing on negative exponents and their implications. The tutorial guides through the process of solving the expression log base 27 of 1/3, ultimately determining that the solution involves a negative exponent. The explanation is detailed, ensuring a clear understanding of the steps involved in solving such logarithmic problems.

What is the relationship between logarithms and exponents?

• Logarithms are the same as exponents.

• Logarithms are only used for base 10 calculations.

• Logarithms are the inverse of exponents.

• Logarithms are unrelated to exponents.

Why must the exponent be negative when converting a larger number to a smaller one using logarithms?

• Because negative exponents result in larger numbers.

• Because negative exponents are not allowed.

• Because negative exponents result in smaller numbers.

• Because negative exponents have no effect.

What happens to a number when it is raised to a negative exponent?

• It becomes zero.

• It remains unchanged.

• It becomes a fraction.

• It becomes a larger number.

How can you express 27 raised to the power of -1/3?

• As 27 cubed.

• As the cube root of 27.

• As the square root of 27.

• As 27 squared.

What is the value of X in the expression log base 27 of 1/3?

• 1/3

• 3

• -1/3

• -1