How do you solve : log(x^2)=(log(x))^2 ? thanks

1 Answer
Apr 11, 2018

color(blue)(x=1 , x=100)x=1,x=100

Explanation:

log(x^2)=(logx)^2log(x2)=(logx)2

I am assuming these to be common logs ( base 10 ):

log(x^2)=2log(x)log(x2)=2log(x)

2log(x)=(log(x))^22log(x)=(log(x))2

(log(x))^2-2log(x)=0(log(x))22log(x)=0

Factor:

log(x)(log(x)-2)=0log(x)(log(x)2)=0

log(x)=0log(x)=0

Using antilogarithm:

10^(log(x))=10^010log(x)=100

x=10^0=1x=100=1

log(x)-2=0log(x)2=0

log(x)=2log(x)=2

10^(log(x))=10^210log(x)=102

x=10^2=100x=102=100

color(blue)(x=1 , x=100)x=1,x=100