Question

if a^2+b^2=23ab show that log (a+b)/5 =1/2(loga+logb)

Answer 1

Answer:

$\displaystyle{}\quad(a+b)^2=a^2+b^2+2ab=23ab+2ab=25ab=5^2ab\\\\\Rightarrow\log(a+b)^2=\log5^2ab\\\\\Rightarrow2\log(a+b)=\log5^2+\log a+\log b\\\\\Rightarrow2\log(a+b)=2\log5+\log a+\log b\\\\\Rightarrow2\log(a+b)-2\log5=\log a+\log b\\\\\Rightarrow\log(a+b)-\log5=\tfrac12(\log a+\log b)\\\\\Rightarrow\log\frac{a+b}5=\tfrac12(\log a+\log b)$

Answer 2

Answer:

.............. hope u understand................