Question1:2^x+y=6,3^x-y=4 find x and y????

Question

quesstion2:a^2+b^2=7ab show that log(a+b)=log3+(loga+logb)/2????

Answer 1

2^x+y = 6
3^x-y = 4

6-2^x = 3^x-4
2^x+3^x = 10
A graphical solution is probably the best bet here.

a^2+b^2=7ab
a^2+2ab+b^2 = 9ab
(a+b)^2 = 9ab
2log(a+b) = log 9ab
log(a+b) = log(9ab)/2
= log√9ab
= log√9 + log√ab
= log3 + log(ab)/2
= log3 + (loga+logb)/2