Logging Now 3

Algebra Level 3

$\frac{1-2(\log x^2)^2}{\log x-2(\log x)^2}=1$ The number of solution(s) for the equation above is?

Note that it is natural logarithm, which has base $e$ .

For more questions on logarithms try this set Logs of logs .

0 4 3 1 2

2 solutions

Paul Ryan Longhas
Apr 6, 2015

Since $\frac{1-2(logx^2)^2}{logx-2(logx)^2}=1$

$\Rightarrow \frac{1-8(logx)^2}{logx - 2(log)^2} = 1$

Let $p$ be equal to $logx$ . Hence

$\frac{1-8p^2}{p-2p^2} = 1$

Massage the equation and solve the value of $p$ .

$\Rightarrow p = \frac{1}{3}, -\frac{1}{2}$

So, $log x =\frac{1}{3}, -\frac{1}{2}$ .

Therefore, they have two solution.

Why 2 solutions? We can't have a logarithm of a negative number right? Or am I missing smth? Thanks in advance for clarifying.

Emmanuel John Baliwag - 6 years, 2 months ago

Yes true we cant have the logarithm of a negative number but here logarithm of a number is negative.

Gautam Sharma - 6 years, 2 months ago

HAHA "Massage the eq" Good one.HAHA

Gautam Sharma - 6 years, 2 months ago

dont you think its over rated???

Prakhar Bindal - 6 years, 2 months ago

What the fffff.... LogX can't negative

I Gede Arya Raditya Parameswara - 4 years, 4 months ago

Kanishk Arora
Apr 7, 2015

truly an overated problem

There is a trick. Inattentive person will spread away the logx=-6/12<0 and keep the logx=4/12>0. log gives a result in whole |R, while defined on |R+*. (Maybe can be used as a test "ware you awaken recently ?")

Leonblum Iznotded - 2 years, 10 months ago

Logging Now 3

For more questions on logarithms try this set Logs of logs .

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