Solving a quadratic Exponential Equation with different bases| Olympiads Exams

How can you solve this interesting Exponential Equation?
In this video, we are going to solve this Olympiads Exponential Equation. All steps needed to solve this problem will be carefully discussed to the understanding of the viewers.
2^X(5^X^2) = 10.
Find the value of X?
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[katemkpani]

You are really improving.

I have just subscribed.
Thank you for all you do.

[icems.a.]

La solución x=1 se puede encontrar reescribiendo la ecuación original
2^x . 5^x^2 = 2.5 , de ahi se deduce x=1

[jpolowin]

There's a notation error at the "x-1 (x log 5 + log 10) = 0" line. It's important to keep the "x-1" in parentheses. Apart from that... very nice!

[justabunga]

Take the log on both sides, which is xlog(2)+x^2log(5)=1. Turn this into a quadratic equation, which is x^2log(5)+xlog(2)-1=0. From there, we need to convert everything with the same log. The LCM of 2 and 5 is 10. Therefore, we can either change log(2)=1-log(5) or log(5)=1-log(2). I'll go with the conversion of log(5)=1-log(2). x^2log(5)+x(1-log(5))-1=0. Turn this into a quadratic formula, which is Simplifying this value will give us The value for x is (2log(5))/(2log(5))=1 and

[social]

the sumnail is wrong. There is 6 instead of 5.