Question

For the equation,
xlog3 x² +(log3 x)^2-10=1÷x^2 is ?​

Answer 1

Answer:

x

log

3

x

2

+(log

3

x)

2

−10

=

x

2

1

For above expression to be defined, x>0

Now take log both sides,

⇒[log

3

x

2

+(log

3

x)

2

−10]logx=log

x

2

1

=−2logx,(loga

n

=nloga)

[log

3

x

2

+(log

3

x)

2

−10]logx+2logx=0

Taking logx common,

logx([log

3

x

2

+(log

3

x)

2

−10]+2)=0

if ⇒logx=0

⇒x=1 ....(1)

or log

3

x

2

+(log

3

x)

2

−10=−2

⇒(log

3

x)

2

+2log

3

x−8=0

⇒log

3

x=−4,2

⇒x=

81

1

,9 ...(2)

From (1) & (2)

x∈{1,9,

81

1

}