Use the properties of logarithms to rewrite and simplify the logarithmic expression.ln6e3

The given expression is ln(6e^3).

We can use the properties of logarithms to simplify this expression.

Step 1: Use the property of logarithms that says the logarithm of a product is the sum of the logarithms.

ln(6e^3) = ln(6) + ln(e^3)

Step 2: Use the property of logarithms that says the logarithm of a number to a power is the power times the logarithm of the number.

ln(6) + ln(e^3) = ln(6) + 3*ln(e)

Step 3: The natural logarithm of e (ln(e)) is 1.

ln(6) + 3ln(e) = ln(6) + 31 = ln(6) + 3

So, the simplified form of the given expression is ln(6) + 3.