Question

Arătați că expresia din poză nu depinde de x​

Answer 1

Răspuns:

$\frac{log3(x)+log3(x^2)+log3(x^7)}{log5(x^2)+log5(x^3)+log5(x^8)}=\frac{log3(x)+2log3(x)+7log3(x)}{2log5(x)+3log5(x)+8log5(x)}=\frac{10log3(x)}{13log5(x)}=\frac{11}{13}* \frac{log3(x)}{log5(x)}$

$=\frac{11}{13}*\frac{1}{log5(3)}$ Done!

Daca te intrebi cum am ajuns la $log5(3)$, am folosit formula de schimbare a bazei. $loga(b)=\frac{logc(b)}{logc(a)}$