Simplify/Condense natural log of 5+5 natural log of 3

Problem

ln(5)+5*ln(3)

Solution

1. Identify the expression as a sum of logarithmic terms.

2. Apply the power property of logarithms, which states n*ln(a)=ln(an) to the second term.

ln(5)+ln(3)

3. Evaluate the exponent 3

3=243

ln(5)+ln(243)

4. Apply the product property of logarithms, which states ln(a)+ln(b)=ln(a*b) to combine the terms.

ln(5⋅243)

5. Multiply the numbers inside the logarithm.

5⋅243=1215

Final Answer

ln(5)+5*ln(3)=ln(1215)

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