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Fri 11 Mar, 2005 05:30 pm
Help?
Find all values of x for which (log x)^3 = 2 log x^2
I would have supposed x = 100, substitute u = log x and solve u^3 = 4u, hence u = 2, and from memory log 100 = 2, so x = 100
Haven't plugged it into a calculator but in my head i got the same thing as g___day so I believe that's right.
x= 1 or 100
am i correct?
getting to basics
& log is common log (base 10)
(logx)^3=2logx^2
(logx)^3=4logx
(logx)^2=4
logx=+/-2
x=100 & x=1/100
although x=1 will work in a pinch because log1=0
Rap
Two of the three, yes
x=1, 100, &/or 1/100
log(1)=0 0^3=4*0
log(100)=2 2^3=4*2
log(1/100)=-2 (-2)^3=4*(-2)
but I can see so far because I stand on your shoulders, Euler.
Rap
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