Question: The given image contains the following text and equations: --- Text: “equation in logarithmic…

The given image contains the following text and equations:

Text: “equation in logarithmic form.”

Equations: \[ \left( \frac{9}{11} \right)^2 = \frac{81}{121} \]

Options:

1. \(\log_{\frac{9}{11}} \frac{81}{121} = 2\)
2. \(\log_{2} \frac{81}{121} = \frac{9}{11}\)
3. \(\log_{\frac{9}{11}} 2 = \frac{81}{121}\)
4. \(\log_{\frac{81}{121}} \frac{9}{11} = 2\)

The image also contains a watermark or text on the right side that reads “Keyboard”.

Solution

To convert the equation \( \left(\frac{9}{11}\right)^2 = \frac{81}{121} \) into logarithmic form, we can follow these steps: Start with the exponential equation: \[ \left(\frac{9}{11}\right)^2 = \frac{81}{121} \] Take the base, \(\frac{9}{11}\), and express the equation in logarithmic form: \[ \log_{\frac{9}{11}} \frac{81}{121} = 2 \] The correct logarithmic form is: \[ \log_{\frac{9}{11}} \frac{81}{121} = 2 \] This corresponds to the first option: \(\log_{\frac{9}{11}} \frac{81}{121} = 2\)