Question

use common logarithms or natural logarithms and a calculator to evaluate the expression.\\(\log_{0.3}29.3\\)\
evaluate the expression.\\(\log_{0.3}29.3\approx\square\\)\
(type an integer or a decimal. do not round until the final answer. then round to four decimal places as needed.)

Explanation:

Step1: Recall Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\log_c a}{\log_c b}$ (where $c$ can be 10 for common logarithms or $e$ for natural logarithms). For $\log_{0.3} 29.3$, we use common logarithms (base 10) or natural logarithms. Let's use common logarithms: $\log_{0.3} 29.3 = \frac{\log 29.3}{\log 0.3}$.

Step2: Calculate Numerator and Denominator

First, calculate $\log 29.3$ (using a calculator, $\log 29.3 \approx 1.46687$). Then, calculate $\log 0.3$ (using a calculator, $\log 0.3 \approx -0.52288$).

Step3: Divide the Two Values

Now, divide the numerator by the denominator: $\frac{1.46687}{-0.52288} \approx -2.8054$.

Answer:

-2.8054