Question

solve for m and n if 4^n × 5^m = 2×10 ^35​

Answer 1

Answer:

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Answer 2

Answer:

First of all we have to resolve this term m = (n² - n - - 35)/(n - 4). arrange the numerator in such a way that it contains (n -4)

Now, n² - n - 35 = n² - 4n+ 3n - 12 - 23 = n(n-4) + 3(n -4) - 23

= (n + 3)(n-4) -23

Hence, m = {(n +3)(n -4) - 23}/(n -4) m = (n +3)(n-4)/(n-4) - 23/(n -4) m = n +3 - 23/(n -4)

m and n both are natural number 23/(n -4) should be natural number it is possible when (n -4)= 23 → n = 27

: m = 27 + 323/23 29

Hence, m = 29 and n = 27