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Mathematics 68 Online
OpenStudy (anonymous):

x^3/2 -27=0 anyone understand this to find the real solution of the equation

OpenStudy (anonymous):

@Tracy 0505 Take log of the equation. so u would get log x^3/2 = log 27 (I took ova the 27). Then apply rule of log so u get 3/2 log x=log 27. This x = e^(2/3 log 27)

OpenStudy (anonymous):

Thanks I think it helps a little.

OpenStudy (anonymous):

slightly simpler x^3/2 =27 (x^3/3)^2/3)=x=27^2/3 don't need to use logs in this case

OpenStudy (anonymous):

typo - (x^3/2)^2/3)=x=27^2/3

OpenStudy (anonymous):

u take the receipcal and it cancels on the left and the right what do u do with it?

OpenStudy (anonymous):

27 cubed the squared?

OpenStudy (anonymous):

by rules of powers , x^(3/2)^2/3)= x^(3/2*2/3) = x^1=x 27^(2/3) = (cube root) squared

OpenStudy (anonymous):

Thanks so much for your time John.

OpenStudy (shadowfiend):

By the way, @Desha, while the log approach is right, remember that the base of log is, by default, 10. So you either $$ x = 10^{\frac{2}{3}\log_{10} 27} $$ Or $$ x = e^{\frac{2}{3}\ln 27} $$ Where ln is the natural log, \(log_e\)

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