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