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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
• 3 values for x. (log can be of any base)

a) log(5)/log(2)

b) log((-5 + i*sqrt(79))/2) / log(2)

c) log ((-5 - i*sqrt(79))/2) / log(2)

8^x + 2^x = 130, can be changed to 2^(3x) + 2^x = 130

Substitute for m = 2^x, rearrange.

m^3 + m - 130 = 0

(m-5)(m^2 + 5m + 26) = 0

3 values of m,

m = 5, m = (-5 + (i*sqrt(79))) / 2, m = (-5 - (i*sqrt(79))) / 2

Substitute it values back to m = 2^x. Apply log of any base.

log(m)/log(2) = x

• 3 values for x. (log can be of any base)

a) log(5)/log(2)

b) log((-5 + i*sqrt(79))/2) / log(2)

c) log ((-5 - i*sqrt(79))/2) / log(2)

8^x + 2^x = 130, can be changed to 2^(3x) + 2^x = 130

Substitute for m = 2^x, rearrange.

m^3 + m - 130 = 0

(m-5)(m^2 + 5m + 26) = 0

3 values of m,

m = 5, m = (-5 + (i*sqrt(79))) / 2, m = (-5 - (i*sqrt(79))) / 2

Substitute it values back to m = 2^x. Apply log of any base.

log(m)/log(2) = x

Children