Question

Compare the numbers 26^39 and 39^26. Which one is bigger? Are they the same? No calculators.

Answer 1

`26^(39)` is greater.

Explanation:

Given numbers,

`26^(39)\text{ and }39^(26)`

∵ HCF ( 26, 39 ) = 13,

That is, we need to make both numbers with the exponent 13.

`26^(39)=((13* 2)^3)^(13)=(13^3* 2^3)^(13)=(13^3* 8)^(13)=(13^2* 104)^(13)`

`(\because (a)^(mn)=(a^m)^n\text{ and }(ab)^m=a^m.a^n)`

`39^(26)=((13* 3)^2)^(13)=(13^2* 3^2)^(13)=(13^2* 9)^(13)`

Since,

`13^2* 104>13^2* 9`

`\implies (13^2* 104)^(13) > (13^2* 9)^(13)`

`\implies 26^(39) > 39^(26)`