logarithmic equations

[jandrisle]

I would appreciate your help again with these logarithmic equations. Honestly, I don't think I know where to start with either of them. These are those end of the chapter problems that the book doesn't give you examples for. Sorry about the formatting.


x^(ln x) = e^(2) * x

I thought maybe start with dividing both sides by x and then taking natural log?

(x^(ln x))/x = e^2
ln (x^(ln x))/x = ln e^2

ln (x^(ln x))/x = 2

Then I get stuck here.......


ln x^(3) = (ln x)^3

This one, I don't even know.

****Thanks for your help****

 

[galactus]

I would appreciate your help again with these logarithmic equations. Honestly, I don't think I know where to start with either of them. These are those end of the chapter problems that the book doesn't give you examples for. Sorry about the formatting.

x^(ln x) = e^(2) * x

I thought maybe start with dividing both sides by x and then taking natural log?

(x^(ln x))/x = e^2
ln (x^(ln x))/x = ln e^2

ln (x^(ln x))/x = 2

Then I get stuck here.......

\(\displaystyle x^{ln(x)}=e^{(ln(x)^{2}}\)

Let u=ln(x)

\(\displaystyle e^{({u})^{2}}=e^{u+2}\)

\(\displaystyle u^{2}=u+2\)




[quote:3f7nnzvt]ln x^(3) = (ln x)^3

This one, I don't even know.

****Thanks for your help****

[/quote:3f7nnzvt]


\(\displaystyle ln(x^{3})=(ln(x))^{3}\)

\(\displaystyle 3ln(x)=(ln(x))^{3}\)

Let u=ln(x)

\(\displaystyle 3u=u^{3}\)

\(\displaystyle u=\pm\sqrt{3} \;\ and \;\ 0\)