SOLUTION: If a^2+b^2 = 7ab, show that log a+b/3=1/2 (loga + logb)

Question 87641: If a^2+b^2 = 7ab, show that log a+b/3=1/2 (loga + logb)
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
Starting with i shall re-write it as .
I am going to prove this is correct instead by looking at the Left hand side and showing that it equals the right hand side .

So,

--> one of laws of Logs
--> multiply out brackets

now we are told that so sub that into what we have and we get:
re-arrange order so you can see the squared terms together
--> sub in the other equality
--> add together like terms
--> cancel out the 9's
use one of the Laws of Logs

which is what i set out to prove it equalled.

cheers
jon

RELATED QUESTIONS
Show that (logb(a))^2(loga(b))^2 =1 (Logb(a))^2 means log base b and same for the... (answered by jim_thompson5910)

Show that logb (a) loga (b) =... (answered by Fombitz,math_helper,MathTherapy)

a^2 + b^2 = 14ab verify log{1/4(a + b) = 1/2(loga +... (answered by Fombitz)

if a^3+b^3=0 then value of log(a+b)-1\2(loga+logb+... (answered by ikleyn)

if log(a+b+c)=loga+logb+logc then prove that log(2a/1-a^2 + 2b/1-b^2 + 2c/1-c^2)= log... (answered by robertb)

if a^2+b^2=7ab,prove that log 1/3(a+b)=1/2[log a+log... (answered by CharlesG2)

If a^2+b^2=7ab,prove that log{1/3(a+b)}=1/2(log a + log b) (answered by ikleyn)

If a^(1/3)+b^(1/3)+c^(1/3)=0, then show that... (answered by orca)

if loga/ b-c = logb/ c-a = logc/ a-b , show that abc =... (answered by robertb)