Logarithmic Properties in Proving Equations

[Sorry!]

Homework Statement

Given a^2+b^2=47ab provehat log((a+b)/7)=1/2(loga+logb)

The Attempt at a Solution

I am assuming it is using multiple log properties... idk how though :|

 

[Astronuc]

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

 

[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)
?

 

[Astronuc]

(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)

 

[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

 

[Astronuc]

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.