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log x = logx (e^4), what is x

Guest Nov 10, 2014

Best Answer 

 #2
avatar+92623 
+10

Maybe you mean

$$\\lnx=log_x(e^4)\\\\
x^{lnx}=x^{log_x(e^4)}\\\\
x^{lnx}=e^4\\\\
ln(x^{lnx})=ln{e^4}\\\\
(lnx)(lnx)=4lne\\\\
(lnx)^2=4\\\\
lnx=2\;\;or\;\;lnx=-2\\\\
x=e^2\;\;\;or\;\;\;x=\frac{1}{e^2}$$

Melody  Nov 10, 2014
 #1
avatar+92623 
+5

$$\\log x = logx \times (e^4)\\$$

there is no soln to this

-------------------------------

Perhaps you mean

$$\\logx = log[x (e^4)]\\
logx = logx +log(e^4)\\$$

No - still no solutions

Melody  Nov 10, 2014
 #2
avatar+92623 
+10
Best Answer

Maybe you mean

$$\\lnx=log_x(e^4)\\\\
x^{lnx}=x^{log_x(e^4)}\\\\
x^{lnx}=e^4\\\\
ln(x^{lnx})=ln{e^4}\\\\
(lnx)(lnx)=4lne\\\\
(lnx)^2=4\\\\
lnx=2\;\;or\;\;lnx=-2\\\\
x=e^2\;\;\;or\;\;\;x=\frac{1}{e^2}$$

Melody  Nov 10, 2014

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