exponents and power question
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0
Answer:
1006
Step-by-step explanation:
Given 9^n+9^n+9^n = 3^2013
=> 3 × 9^n = 3^2013
=> 3 × (3^2)^n = 3^2013
=> 3× 3^2n = 3^2013 [ Since (x^a)^b = x^ab
=> 3^(1+2n) = 3^2013 [ Since x^a × x^b = x^(a+b)
By comparing the powers of 3 on both the sides, we get
=> 1+2n = 2013
=> 2n = 2013 - 1
=> 2n = 2012
By dividing by 2 on both the sides, we get
=> n = 2012/2
=> n = 1006 Answer.
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