Question

$Aratati ~ca~: \\ \\ ( \frac{b}{c} )^{lga} *( \frac{c}{a})^{lgb}*( \frac{a}{b} )^{lgc}=1.$

Answer 1

Am atasat rezolvarea.

Eu am aplicat formula doar pentru numaratori, si s-au simplificat fiecare cu cate un numitor.

Answer 2

$\displaystyle Coincidenta~face~ca~am~avut~aceasta~problema~la~un~test. \\ \\ Am~dat~urmatoarea~solutie: \\ \\ Notam~u= \lg a,~v= \lg b~si~w= \lg c. \\ \\ Obtinem~a=10^u,~b=10^v,~c=10^w. \\ \\ Solutia~(propriu-zisa): \\ \\ E= \left( \frac{10^v}{10^w} \right)^u \cdot \left( \frac{10^w}{10^u} \right)^v \cdot \left( \frac{10^u}{10^v} \right)^w= \\ \\ =10^{u(v-w)} \cdot 10^{v(w-u)} \cdot 10^{w(u-v)}= \\ \\ =10^{u(v-w)+v(w-u)+w(u-v)}= \\ \\ =1.$