Question

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

Answer 1

Answer:

$26^{39}$ is greater.

Step-by-step 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.

$26^{39}=((13\times 2)^3)^{13}=(13^3\times 2^3)^{13}=(13^3\times 8)^{13}=(13^2\times 104)^{13}$

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

$39^{26}=((13\times 3)^2)^{13}=(13^2\times 3^2)^{13}=(13^2\times 9)^{13}$

Since,

$13^2\times 104>13^2\times 9$

$\implies (13^2\times 104)^{13} > (13^2\times 9)^{13}$

$\implies 26^{39} > 39^{26}$