Question

10 la puterea 2n+1:5la puterea 2n+1=8 la puterea 9. Va rog sa m-a ajutați,mulțumesc!

Answer 1

 [tex]10^{2n+1}=(2\cdot5)^{2n+1}=2^{2n+1}\cdot5^{2n+1}\,\\ \Rightarrow\,\,(2^{2n+1}\cdot5^{2n+1}):5^{2n+1}=2^{2n+1}[/tex]
[tex]\Rightarrow\,2^{2n+1}=8^9=2^{3\cdot9}\,\,\\ Inseamna\,ca\,\,puterea\,2n+1=27\,\,\,adica:\,\fbox{n=13}[/tex]

Answer 2

10 la 2n+1=[2·5] la 2n+1;
⇒[2·5] la 2n+1 /5 la 2n+1=2 la 2n+1;
⇒2 la 2n+1=2²⁷⇒2n+1=27⇒2n=26⇒n=13;