Question

if (25)n x (31)n =(1015)n then the value of (13)n x (52)n is when n>0

Answer 1

25n × 31n = 1015n

=> divide both sides by 5

=> 25n × 31n ÷ 5 = 1015 ÷ 5

=> 155n^2 = 203n

=> 155n^2 - 203n = 0

=> factor out n from the expression

=> n( 155n - 203) = 0

=> when the product of factors equal to 0, atleast 1 factor is 0

=> n = 0

【 but as given n > 0 】

so,

=> 155n - 203 = 0

=> 155n = 203

=> n = 203 ÷ 155 or 203/155

=> n = 1.30968


Value of 13n × 52n =>

To find the value of the expression put the value of n in the expression

=> 13(203/155)×52(203/155)

=> 27857284/24025

=> 1159.512 (approx)

Answer 2

I have given the answer in the images.

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