log 49
3√7

Q: log 49 3√7

The expression in the image is $ \log_{49} \sqrt[3]{7} $. To solve this, you can use the change of base formula and properties of logarithms: 1. **Change of Base Formula:** \[ \log_{49} \sqrt[3]{7} = \frac{\log_{10} \sqrt[3]{7}}{\log_{10} 49} \] 2. **Simplify the Numerator:** \[ \log_{10} \sqrt[3]{7} = \log_{10} (7^{1/3}) = \frac{1}{3} \log_{10} 7 \] 3. **Simplify the Denominator:** \[ \log_{10} 49 = \log_{10} (7^2) = 2 \log_{10} 7 \] 4. **Combine the Expressions:** \[ \log_{49} \sqrt[3]{7} = \frac{\frac{1}{3} \log_{10} 7}{2 \log_{10} 7} = \frac{1}{6} \] Thus, the value of $ \log_{49} \sqrt[3]{7} $ is $\frac{1}{6}$.

Question

log 49
  3√7

Accepted Answer

The expression in the image is $ \log_{49} \sqrt[3]{7} $.

To solve this, you can use the change of base formula and properties of logarithms:

1. **Change of Base Formula:**
   $$
   \log_{49} \sqrt[3]{7} = \frac{\log_{10} \sqrt[3]{7}}{\log_{10} 49}
   $$

2. **Simplify the Numerator:**
   $$
   \log_{10} \sqrt[3]{7} = \log_{10} (7^{1/3}) = \frac{1}{3} \log_{10} 7
   $$

3. **Simplify the Denominator:**
   $$
   \log_{10} 49 = \log_{10} (7^2) = 2 \log_{10} 7
   $$

4. **Combine the Expressions:**
   $$
   \log_{49} \sqrt[3]{7} = \frac{\frac{1}{3} \log_{10} 7}{2 \log_{10} 7} = \frac{1}{6}
   $$

Thus, the value of $ \log_{49} \sqrt[3]{7} $ is $\frac{1}{6}$.

log 49 3√7

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