Express 2 ln(3) + ln(11) as a single natural logarithm

To simplify this equation we need to understand the rules of logarithm equations. When we add two natural logs (ln) together, we must actually multiply the contents of the brackets. For example:ln(5) + ln(9) = ln(5 x 9) = ln(45)Another rule to note when addressing this question, is the prefix to the natural log. This is the number before the natural log. This number is actually used as a power to the number within the brackets. For example:4ln(2) = ln(2^4) = ln(16)This rule is therefore useful in simplifying the natural logarithm. Now, with the rules that I have just discussed, the question can be answered.{ANSWER: 2ln(3) + ln(11) = ln(3^2) + ln(11) = ln(9) + ln(11) = ln(11*9) = ln(99)}

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Answered by Jordan K. Maths tutor

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