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QUESTION

# How do you solve for x in 1/3lnx+ln2-ln3=3?

The answer is: x=27/8e^9.

First of all we have to add a condition otherwise our equation loses meaning: x>0.

Than:

1/3lnx+ln2-ln3=3rArrlnx=3(ln3-ln2+3)rArr

lnx=3(ln3-ln2+lne^3)rArrlnx=3ln(3e^3/2)rArr

lnx=ln(27/8e^9)rArrx=27/8e^9

(That is positive, so it is acceptable).