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If ln a = 2  and ln b = 3 find the value of the equation ln (a^2/b^3).

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clara2 | Student, Undergraduate | eNoter

Posted February 10, 2011 at 12:15 PM via web

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If ln a = 2  and ln b = 3 find the value of the equation ln (a^2/b^3).

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted February 10, 2011 at 12:19 PM (Answer #1)

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Given that :

ln a = 2

ln b = 3

We need to find the values of ln a^2/b^3

We will use the logarithm properties to solve.

We know that ln a/b = ln a - ln b

Then we will simplify:

ln a^2/b^3 = ln a^2 - ln b^3

Now we also know that ln x^a = a*ln x

==> ln a^2 - ln b^3 = 2*ln a - 3*ln b

Now we will substitute with the value of ln a and ln b

==> ln (a^2/b^3) = 2*2 - 3*3 = 4- 9= -5

Then the value of ln (a^2/b^3) = -5.

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