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# KCC's Quizzes AQQ253 about a funny equation

And here is a new challenge! It's easier than the previous one but still...

Also, please be informed awards and goodies are being sent to the frequent winners. Please apologize for the long delay since we do that only 2 times per year!

Certificates of the wins are also sent in paper form; the ones desiring a digital copy, please let us know!

Some statistics about the frequent winners by country origins: (we have also statistics by individuals, but they can be provided on demand and only with own data).

Regards

Kuo-Chang

Parents
• 8^x + 2^x = 130

Assume 2^x = t then the equation will become t^3+t-130 = 0

So possible value of t will be 5 so then equation will be (t - 5) (t^2+5t+26) = 0.

And t^2+5t+26 will give us imaginary roots because discrimant is 5*5-4*1*26 which is negative so possible value of t is 5

Hence value of x is log5/log2 which is 2.3219

Ans 2.3219

• Thnaks  fr your prompt feedback!

Yes, 2.3219 is indeed a solution to the equation. BUT there are others! The question was saying all the possible solutions for x (not necessarily real numbers!). may be you can retreive them?

• Thnaks  fr your prompt feedback!

Yes, 2.3219 is indeed a solution to the equation. BUT there are others! The question was saying all the possible solutions for x (not necessarily real numbers!). may be you can retreive them?

Children
• So we can get value of t as (-5+i√79) /2 and  (-5-i√79) /2 so value of x will be log( -5+i√79) /2*log2 and  (-5-i√79) /2*log2.

Not sure if we can calculate further.