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anonymous
 one year ago
Solve for x (IB HL Math question)
anonymous
 one year ago
Solve for x (IB HL Math question)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\Large \ln(x)+\log_{x}\sqrt{e}=\frac{1}{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@CandyCove @CBARREDO1 @Loser66 @LynFran @pooja195

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh I figured it out. Change of base formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I aso wrote the wrong problem. This one gives imag solutions \[\Large \ln(x)+\log_{x}\sqrt{e}=\frac{3}{2}\]

dan815
 one year ago
Best ResponseYou've already chosen the best response.0ya apply change of base and u can play around with it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So \[\Large 2\ln(x)+\frac{\ln(e)}{\ln(x)}=3\]

dan815
 one year ago
Best ResponseYou've already chosen the best response.0multiply everything by ln(x) and set y = ln(x) solve for y for the quadratic u get then solve for x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and then \[\Large 2(lnx)^{2}+1=3\ln(x)\] If we set (lnx)=x \[\Large 2(x)^23(x)+1=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Quad formula gives us x=1 and x=1/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So pluggin x back in gives us lnx=1 and lnx=1/2 x= e and x= sqrt(e)

dan815
 one year ago
Best ResponseYou've already chosen the best response.0plug in your answers to check

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ln(e)+log_e{sqrt{e}}= 1 + 1/2 = 3/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ln(sqrt(e)}+log_sqrt(e)(sqrt(e)}= 1/2 +1 = 3/2
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