6 Use a log property to find the exact va log816log82 7 Solv

6. Use a log property to find the exact va log816-log82 7. Solve the equations. Give exact and a) 2log3(x +4)-log39 2 Domain/k K21

Solution

2log₃(x+4)-log₃9=2

log₃(x+4)²- log₃9=2

log₃((x+4)²/9)=2

(x+4)²/9 = 9

(x+4)²=81

x+4=-9 , x+4=9

x=-13, x=5

log cant take negative value

So the answer is x=5

Domain

Log cant take 0 or less tan 0

x+4>0

x>-4

Domain (-4,infinity)