How do you evaluate log₀.₈(12)?

To evaluate the logarithm log₀.₈(12), you can use the change of base formula, which allows you to convert the logarithm to a more manageable base. The formula is:

Change of Base Formula

The change of base formula states:

log_b(a) = log_c(a) / log_c(b)

Here, you can choose any base c, commonly 10 or e (natural logarithm).

Applying the Formula

For log₀.₈(12), we can use base 10:

log₀.₈(12) = log(12) / log(0.8)

Calculating the Values

• Calculate log(12) using a calculator, which is approximately 1.0792.
• Calculate log(0.8), which is approximately -0.0969.

Final Calculation

Now, divide the two results:

log₀.₈(12) ≈ 1.0792 / -0.0969 ≈ -11.13

Thus, the value of log₀.₈(12) is approximately -11.13.