Question 410617
"I really need help solving this equation. PLEASE help?

ln(x+1)-ln(x-2)=ln(5)

1. Solve equation by setting up algebraically.
2. Use appropriate properties of Logarithm to reduce the number of logarithmic terms to only one.
3. Solve logarithmic equation. "


ln(x + 1) - ln(x - 2) = ln(5)
logarithmic rule: ln(m) - ln(n) = ln(m/n)
ln((x + 1)/(x - 2)) = ln(5)
(x + 1)/(x - 2) = 5 (what was in parentheses on above line must equal)
x + 1 = 5(x - 2)
x + 1 = 5x - 10
-4x = -11
x = 11/4
check:
ln(11/4 + 1) - ln(11/4 - 2) = ln(5)
ln(11/4 + 4/4) - ln(11/4 - 8/4) = ln(5)
ln(15/4) - ln(3/4) = ln(5)
ln(15/4 * 4/3) = ln(5)
ln(15/3) = ln(5)
ln(5) = ln(5) , yes