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

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Answer 1 · 2018-04-11T22:05:47

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

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

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

#log(x^2)=2log(x)#

#2log(x)=(log(x))^2#

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

Factor:

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

#log(x)=0#

Using antilogarithm:

#10^(log(x))=10^0#

#x=10^0=1#

#log(x)-2=0#

#log(x)=2#

#10^(log(x))=10^2#

#x=10^2=100#

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