How do you solve 2 log x = log 25 + 22logx=log25+2?

1 Answer
Dec 29, 2015

Use the fact that log(x)log(x) is a one-one function as a Real-valued function of Real numbers to find:

x = 50x=50

Explanation:

Divide both sides by 22 to get:

log(x)log(x)

= (log(25)+2) / 2=log(25)+22

= (2 log(5) + 2 log(10))/2=2log(5)+2log(10)2

= log(5) + log(10)=log(5)+log(10)

= log(50)=log(50)

Hence x = 50x=50, since log(x):(0, oo) -> RR is one-one.