Question

Daca numarul 2 la puterea 2015 are A cifre si numarul 5 la puterea 2015 are B cifre ,determinati A+B.

Answer 1

daca nr $2^{2015}$ are A cifre inseamna ca $10^{A-1}\ \textless \ 2^{2015}\ \textless \ 10^{A}$
Analog $10^{B-1}\ \textless \ 5^{2015}\ \textless \ 10^{B}$
Inmultim relatiile si avem:
$10^{A+B-2} \ \textless \ 10^{2015} \ \textless \ 10^{A+B}$
Deci 2015= A+B-1, A+B=2016