Question

How do you evaluate log_3 (1/243)?

Answer 1

To evaluate log_3 (1/243), recognize that 243 is 3^5, convert 1/243 to 3^-5, and apply logarithmic properties to simplify log_3(3^-5) to -5.

Step-by-step explanation:

To evaluate log_3 (1/243), we first need to recognize that 243 is a power of 3: 243 = 3^5. The logarithm asks the question: to what power do we raise 3 to obtain 1/243? Since 1/243 is the same as 3^-5 (since taking the reciprocal inverts the exponent), we have log_3(3^-5).

By the properties of logarithms, specifically the property that log base b of (b^x) = x, we can simplify our expression to -5.

In short:

1. Recognize that 243 is 3^5.
2. Convert 1/243 to 3^-5.
3. Apply the logarithmic property to get the answer, which is -5.