Question

Rewrite the following in logarithmic form: 8³ = 512.

a. log₈ 512 = 3
b. log₃ 512 = 8
c. log₅₁₂ 8 = 3
d. log₈ 3 = 512

Answer 1

To convert the exponential expression 8³ = 512 to logarithmic form, identify the base, exponent, and result, and express them in the form log_base(result) = exponent, which results in log₈ 512 = 3.

Step-by-step explanation:

The question requires converting the exponential form 8³ = 512 into logarithmic form. The base, exponent, and the result in an exponential equation correspond to different parts of a logarithmic equation. Specifically:

• The base of the exponent becomes the base in the logarithm.
• The exponent is the value that the logarithm is equal to.
• The result of the exponentiation becomes the number for which we are taking the logarithm.

Using this understanding, the exponential equation 8³ = 512 would translate into logarithmic form as log₈ 512 = 3. This reads as 'The logarithm base 8 of 512 equals 3,' which means that you have to raise the number 8 to the power of 3 to get 512. Therefore, the correct answer is option a: log₈ 512 = 3.