To evaluate \( \log 3\sqrt{100} \), we first need to simplify the expression inside the logarithm. 1. **Simplify the square root:** \[ \sqrt{100} = 10 \] Therefore, we can rewrite the expression as: \[ \log 3\sqrt{100} = \log (3 \cdot 10) = \log 30 \] 2. **Logarithm Value:** Depending on the base of the logarithm you're using (common logarithm base 10, natural logarithm base \( e \), etc.), you can evaluate \( \log 30 \) using a calculator or logarithmic properties. If you simply need the expression, you can stop here. If you need a numerical value, you can calculate \( \log_{10} 30 \) using a scientific calculator: \[ \log_{10} 30 \approx 1.477 \] Thus, \[ \log 3\sqrt{100} = \log 30 \approx 1.477 \]

Evaluate log 3√100

1 answer

To evaluate \( \log 3\sqrt{100} \), we first need to simplify the expression inside the logarithm.

Simplify the square root: \[ \sqrt{100} = 10 \] Therefore, we can rewrite the expression as: \[ \log 3\sqrt{100} = \log (3 \cdot 10) = \log 30 \]
Logarithm Value: Depending on the base of the logarithm you're using (common logarithm base 10, natural logarithm base \( e \), etc.), you can evaluate \( \log 30 \) using a calculator or logarithmic properties. If you simply need the expression, you can stop here.

If you need a numerical value, you can calculate \( \log_{10} 30 \) using a scientific calculator: \[ \log_{10} 30 \approx 1.477 \]

Thus, \[ \log 3\sqrt{100} = \log 30 \approx 1.477 \]