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can u solve this simultaneous equation?
lg x + 2lg y = 3
x^2 (y) =125
p.s. x^2 meaning x square...
Thanks
2 réponses
- LearnerLv 7il y a 8 ansRéponse favorite
i) It is given lg; so let me take this as base 10 and not as e.
[For taking base e, generally it will be mentioned as ln]
ii) 2log(y) = log(y²) [Application of power law of log]
log(x) + 2log(y) = log(x) + log(y²) = log(xy²) [Application of product law of log]
So as given log₁₀(xy²) = 3
Hence, by definition of log, xy² = 10³ = 1000 ------ (1)
iii) Given x²y = 125 ---- (2)
iv) Dividing (1) by (2): y/x = 8; ==> y = 8x
Substituting in (2) above, 8x³ = 125
Taking cube root on both sides, 2x = 5
==> x = 5/2; so y = 8x = 8*(5/2) = 20
Thus x = 5/2 and y = 20
- ?Lv 6il y a 8 ans
Logxy^2=3
xy^2=e^3-------(1) x^2y=125-------(2) so x^3y^3=125e^3 so xy=5e ----(3)
x^2y/xy=125/5e
x=25/e xy^2/xy=e^3/5e so y=e^2/5