Simplify/Condense log base 7 of 49x

Problem

(log_7)(49*x)

Solution

1. Identify the logarithmic property for the logarithm of a product, which states (log_b)(M*N)=(log_b)(M)+(log_b)(N)

2. Apply the property to the expression by splitting the product 49*x into two separate logarithms.

(log_7)(49*x)=(log_7)(49)+(log_7)(x)

3. Evaluate the numerical logarithm by recognizing that 49 is a power of the base 7 specifically 49=7

(log_7)(7)=2

4. Substitute the simplified value back into the expression.

2+(log_7)(x)

Final Answer

(log_7)(49*x)=2+(log_7)(x)

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