Let 2^x= a, 5^x=b You will get a quadratic equation (a/b)^2-6(a/b)+1=0 Solve for a/b and substitute ,you will get a/b = 5.828 or a/b= 0.1716 Apply log for both sides and solve for x , take the positive value only X= 1.92
I appreciate your sharing your approach to solving this problem! It's always fascinating to see different ways to tackle math challenges. Thanks for pointing out this alternative solution! It seems very efficient. 👍💖💯
Cool problem. Question: What precludes x from having a negative value? We could choose the negative value of Sqrt(10^x) and the math would work. Is this just a matter of convention? I solved in a similar way but left it at m= 3+/- 2sqrt(2). The negative m was disqualified as it went inside the argument in a logarithm. By completing the square you no longer have a negative inside a log expression. But then you rejected the negative value for x without explaining why. Finding this extra solution justified the extra work imo.
Лишние замены
Разделили на 2^х
(5/2)^х-1=2*sqrt (5/2)^x
Замена sqrt((5/2)^х)=а>0
a^2-1+2a=0
Обычное квадратное уравнение
Let 2^x= a, 5^x=b
You will get a quadratic equation
(a/b)^2-6(a/b)+1=0
Solve for a/b and substitute ,you will get
a/b = 5.828 or a/b= 0.1716
Apply log for both sides and solve for x , take the positive value only
X= 1.92
I appreciate your sharing your approach to solving this problem! It's always fascinating to see different ways to tackle math challenges. Thanks for pointing out this alternative solution! It seems very efficient. 👍💖💯
Cool problem.
Question: What precludes x from having a negative value? We could choose the negative value of Sqrt(10^x) and the math would work. Is this just a matter of convention?
I solved in a similar way but left it at m= 3+/- 2sqrt(2). The negative m was disqualified as it went inside the argument in a logarithm. By completing the square you no longer have a negative inside a log expression. But then you rejected the negative value for x without explaining why. Finding this extra solution justified the extra work imo.
Ludzie! To troll. On rozwiązuje zadania jak najdłużej można, olewa krótsze metody, by mieć długie oglądalności nieco zarobić na reklamach.