Note that \(x=5\) is a repeated root so the differential would be 0 at \(x=5\). Try to plot the graph. At \(x=\infty,\ LHS=\infty\). At \(x=5,6,2\), \(LHS=0\). At \(x=0,\ LHS>0\). I think graphs can be plotted now and it will intersect \(y=\ln x\) at two points.

I'll post more tomorrow, but for now, I'd just say to create a sign chart of where the exponent and where the \(x^2-7x+11\) are positive and when negative and where the LHS exceeds the RHS. The problem is that if the LHS intersects the RHS when negative, You have to watch for extraneous solutions because \((-2)^{\frac{7}{12}}\) is not an answer since its imaginary (the answer isn't 2^7/12, Im just using it as an example.

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestTaking log both sides,

\((x-5)(x-6)\ln (x^2-7x+11)=\ln x\)

Note that \(x=5\) is a repeated root so the differential would be 0 at \(x=5\). Try to plot the graph. At \(x=\infty,\ LHS=\infty\). At \(x=5,6,2\), \(LHS=0\). At \(x=0,\ LHS>0\). I think graphs can be plotted now and it will intersect \(y=\ln x\) at two points.

Log in to reply

@Chew-Seong Cheong @Aneesh Kundu @Pranjal Jain @megh choksi @Jon Haussmann @Trevor Arashiro @Trevor B. @Calvin Lin @Aman Sharma Please upload solution if u can

Log in to reply

I'll post more tomorrow, but for now, I'd just say to create a sign chart of where the exponent and where the \(x^2-7x+11\) are positive and when negative and where the LHS exceeds the RHS. The problem is that if the LHS intersects the RHS when negative, You have to watch for extraneous solutions because \((-2)^{\frac{7}{12}}\) is not an answer since its imaginary (the answer isn't 2^7/12, Im just using it as an example.

Log in to reply