25^n × 5 × 5^n - 125^n / 125^m × 2^2 = 1/125
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Answers
Given: The term (25^n × 5 × 5^n - 125^n) / (125^m × 2^2) = 1/125
To find: Find the relation between m and n.
Solution:
- Now we have given:
(25^n × 5 × 5^n - 125^n) / (125^m × 2^2) = 1/125
- We can rewrite it as:
((5^2)^n × 5^(n+1) - (5^3)^n) / ((5^3)^m × 4) = 1/5^3
(5^2n × 5^(n+1) - 5^3n) / (5^3m × 4) = 5^-3
(5^3n × 5 - 5^3n) / (5^3m × 4) = 5^-3
(5^3n × (5 - 1) ) / (5^3m × 4) = 5^-3
(5^3n × 4 ) / (5^3m × 4) = 5^-3
(5^3n / 5^3m) = 5^-3
(5^(3n-3m)) = 5^-3
- As now the base is same, i.e. 5, so equating the powers, we get:
3n-3m = -3
3m - 3n = 3
m - n = 1
Answer:
So the relation between m and n is m-n = 1.
Answer:
Given: The term (25^n × 5 × 5^n - 125^n) / (125^m × 2^2) = 1/125
To find: Find the relation between m and n.
Solution:
Now we have given:
(25^n × 5 × 5^n - 125^n) / (125^m × 2^2) = 1/125
We can rewrite it as:
((5^2)^n × 5^(n+1) - (5^3)^n) / ((5^3)^m × 4) = 1/5^3
(5^2n × 5^(n+1) - 5^3n) / (5^3m × 4) = 5^-3
(5^3n × 5 - 5^3n) / (5^3m × 4) = 5^-3
(5^3n × (5 - 1) ) / (5^3m × 4) = 5^-3
(5^3n × 4 ) / (5^3m × 4) = 5^-3
(5^3n / 5^3m) = 5^-3
(5^(3n-3m)) = 5^-3
As now the base is same, i.e. 5, so equating the powers, we get:
3n-3m = -3
3m - 3n = 3
m - n = 1
Answer:
So the relation between m and n is m-n = 1.
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