Question

solve for x
ln x= ln(x+6)-ln 5

Answer 1

use the theorem\[\ln(u)=\ln(v) \iff u=v\]

Answer 2

\[\ln x=\ln \frac{x+6}{5}\]now use the theorem\[x=\frac{x+6}{5}\]and solve this\[5x=x+6\]\[4x=6\]\[x=3/2\]when you solve log equations you always have to remeber to check back to see about any domain issues; you can only take the log of a positve; so we need to check the x=3/2 to be certain that it does not make any of the arguments < or = 0

Answer 3

check: ln(3/2) is ok and ln(3/2+6) is ok so the solution set is {3/2}