Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F142e1ae3-c931-47e5-a8d0-830705d30c68%2F2f6db72c-5e78-459e-b827-5d533ed856e1%2Fxkm8y0a_processed.jpeg&w=3840&q=75)
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