Questions: Question 12 Use common logarithms or natural logarithms and a calculator to evaluate the expression log15 12 Evaluate the expression. log15 12 ≈ (Type an integer or a decimal. Do not round until the final answer. Then round to

Solution Steps

To evaluate \(\log_{15} 12\), we can use the change of base formula, which states:

\[ \log_{b} a = \frac{\log_{c} a}{\log_{c} b} \]

where \(c\) is any positive number different from 1. Common choices for \(c\) are 10 (common logarithm) or \(e\) (natural logarithm). Here, we will use the common logarithm (base 10).

Using the change of base formula with base 10, we have:

\[ \log_{15} 12 = \frac{\log_{10} 12}{\log_{10} 15} \]

Using a calculator, we find:

\[ \log_{10} 12 \approx 1.0792 \] \[ \log_{10} 15 \approx 1.1761 \]

Now, divide the two results:

\[ \log_{15} 12 \approx \frac{1.0792}{1.1761} \approx 0.9173 \]

Final Answer