Question

A6, subpunctele b si d. (d-ul e pe cealaltă parte, l-am pus separat în poză)
Ofer coroană+60 de puncte.

Answer 1

Salut,

Folosim formula de schimbare de variabilă:

$log_ab=\dfrac{log_cb}{log_ca};\\\\B=\dfrac{\dfrac{lnx}{ln2}+\dfrac{lnx}{ln4}+\dfrac{lnx}{ln16}}{\dfrac{lnx}{ln5}+\dfrac{lnx}{ln25}+\dfrac{lnx}{ln0,2}}=\dfrac{lnx\cdot\left(\dfrac{1}{ln2}+\dfrac{1}{ln4}+\dfrac{1}{ln16}\right)}{lnx\cdot\left(\dfrac{1}{ln5}+\dfrac{1}{ln25}+\dfrac{1}{ln0,2}\right)}=\\\\\\=\dfrac{\dfrac{1}{ln2}+\dfrac{1}{ln4}+\dfrac{1}{ln16}}{\dfrac{1}{ln5}+\dfrac{1}{ln25}+\dfrac{1}{ln0,2}}, \care\ nu\ mai\ depinde\ de\ x,\ ceea\ ce\ trebuia\ demonstrat.$

Green eyes.