What is 3 ln 3 - ln 9 expressed as a single natural logarithm?

Mathematics

2 answers:

Elina [12.6K]3 years ago

5 0

Answer: 3

Step-by-step explanation:

marusya05 [52]3 years ago

4 0

Answer: In 3
SOLVINGS
What is 3 ln 3 - ln 9 expressed as a single natural logarithm

Since ln (m^n) = n⋅ln (m) … natural logarithmic property
We can further simplify the expression 3 ln 3
3 In 3 = In (3^3)
Therefore, 3 ln 3 - ln 9 = In (3^3) – In 9

Since ln(m/n) =ln(m) – ln(n) … natural logarithmic property
We can further simplify the expression In (3^3) – In 9
In (3^3) – In 9 = In [(3^3)/(9)]
= In (27/9)
= In 3

Therefore, 3 ln 3 - ln 9 expressed as a single natural logarithm is In 3.

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