Homework Help: Using multiple log properties

1. Nov 7, 2007

Sorry!

1. The problem statement, all variables and given/known data
Given a^2+b^2=47ab provehat log((a+b)/7)=1/2(loga+logb)

3. The attempt at a solution
I am assuming it is using multiple log properties... idk how though :|

2. Nov 7, 2007

Astronuc

Staff Emeritus
What can be added to both sides such that a^2+b^2 can be become (a+b)2?

3. Nov 7, 2007

Sorry!

ooooooh so is this right?

(a+b)^2=49ab
a+b=7(ab)^(1/2)
(a+b)/7=(ab)^1/2

log((a+b)/7)=1/2(loga+logb)
???

4. Nov 8, 2007

Astronuc

Staff Emeritus
(a+b)^2=49ab
a+b=7(ab)^(1/2)
(a+b)/7=(ab)^1/2

so log [ (a+b)/7 ] = log [ (ab)^(1/2)]

log (ab)^1/2 = 1/2 log ab = 1/2 (log a + log b)

5. Nov 8, 2007

Sorry!

yeah i got it :D

man that was so easy. i feel so stupid took 0/6 on my test ha :|

thanks for the help astronuc

6. Nov 8, 2007

Astronuc

Staff Emeritus
Yeah - one just has to learn to think about factoring things and sometimes adding or subtracting from both sides of an equation to simplify it, or add, subtract and regroup on the same side.