Simplify/Condense natural log of x+ natural log of 19

Problem

ln(x)+ln(19)

Solution

1. Identify the logarithmic property for addition, which states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments.

2. Apply the Product Rule for logarithms, which is defined as ln(a)+ln(b)=ln(a*b)

3. Substitute the given values a=x and b=19 into the formula.

4. Simplify the resulting expression by writing the constant coefficient before the variable.

Final Answer

ln(x)+ln(19)=ln(19*x)

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