Find x in log ⁡ x 2 = ( log ⁡ x ) 2 I couldn't find x.

log ⁡ x 2 = ( log ⁡ x ) 2 2 log ⁡ x = ( log ⁡ x ) 2 log ⁡ x ( log ⁡ x − 2 ) = 0 log ⁡ x = 0 → x = 1 log ⁡ x = 2 → x = 10 2

Hint: Note that log ⁡ x 2 = 2 log ⁡ xfor all x &gt; 0. Now use the substitution u = log ⁡ x to get 2 u = u 2 .Solve for u , then solve for x .

log ⁡ x 2 = ( log ⁡ x ) 2 2 log ⁡ x = ( log ⁡ x ) 2 log ⁡ x ( log ⁡ x − 2 ) = 0 log ⁡ x = 0 → x = 1 log ⁡ x = 2 → x = 10 2

Hint: Note that log ⁡ x 2 = 2 log ⁡ xfor all x &gt; 0. Now use the substitution u = log ⁡ x to get 2 u = u 2 .Solve for u , then solve for x .

We have an answer to "Find x in log ⁡ x 2 =..."

Frank Day

2022-07-02

Find

x

\log x^{2} = (\log x)^{2}

I couldn't find x.

Bruno Dixon

Beginner2022-07-03Added 14 answers

\log x^{2} = (\log x)^{2} 2 \log x = (\log x)^{2} \log x (\log x - 2) = 0 \log x = 0 \to x = 1 \log x = 2 \to x = 10^{2}

Patatiniuh

Beginner2022-07-04Added 5 answers

Hint: Note that

\log x^{2} = 2 \log x

for all

x > 0.

Now use the substitution

u = \log x

to get

2 u = u^{2} .

Solve for

u,

then solve for

x .

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?