Please help/show work.23 **Condense the logarithmic expression below.**\[ \log_7 2 + 2 \log_7 6 - \log_7 9 \]To condense the logarithmic expression given, we can use the properties of logarithms:1. **Product Property of Logarithms:**\[ \log_b M + \log_b N = \log_b (MN) \]2. **Power Property of Logarithms:**\[ a \log_b M = \log_b (M^a) \]3. **Quotient Property of Logarithms:**\[ \log_b M - \log_b N = \log_b \left( \frac{M}{N} \right) \]**Step-by-Step Solution:**1. Apply the Power Property to the second term:\[ 2 \log_7 6 = \log_7 (6^2) = \log_7 36 \]2. Replace the second term in the original expression:\[ \log_7 2 + \log_7 36 - \log_7 9 \]3. Combine the first two terms using the Product Property:\[ \log_7 (2 \cdot 36) - \log_7 9 = \log_7 72 - \log_7 9 \]4. Finally, apply the Quotient Property to condense the expression:\[ \log_7 \left( \frac{72}{9} \right) = \log_7 8 \]So, the condensed form of the original logarithmic expression is:\[ \log_7 8 \]This transformation utilizes logarithmic properties to condense multiple logarithmic terms into a single logarithmic expression.

Name: Please help/show work.23 **Condense the logarithmic expression below.*
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Please help/show work.23 **Condense the logarithmic expression below.**\[ \log_7 2 + 2 \log_7 6 - \log_7 9 \]To condense the logarithmic expression given, we can use the properties of logarithms:1. **Product Property of Logarithms:**\[ \log_b M + \lo