Simplify/Condense 2 natural log of e^6- natural log of e^5

Problem

2*ln(e^6)−ln(e^5)

Solution

1. Apply the power property of logarithms to the first term, which states a*ln(b)=ln(b^a)

ln((e^6)^2)−ln(e^5)

2. Simplify the exponent using the power of a power rule (x^a)^b=x^(a*b)

ln(e^12)−ln(e^5)

3. Apply the quotient property of logarithms, which states ln(a)−ln(b)=ln(a/b)

ln((e^12)/(e^5))

4. Simplify the fraction by subtracting the exponents of the base e

ln(e^7)

5. Apply the inverse property of natural logarithms, where ln(e^x)=x

7

Final Answer

2*ln(e^6)−ln(e^5)=7

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