Question

Find n in the equation
5raise to 2,× 5raise to 4 ×5 raise to 6.....×5 raise to 2n =(125)30

Answer 1

Answer: n= 9 or -10

Step-by-step explanation:

5^2× 5^4× 5^6× .......... × 5^(2n) = (125)^30

5^(2+4+6+........+2n) = (5×5×5) ^30

5^(2+4+6+........+2n) = 5^(3×30)

5^2(1+2+3+4+........+n) = 5^90

Now, 1+2+3+4+....+n=n(n+1) /2

2(1+2+3+4+....+n)=n(n+1)

Hence, 5^2(1+2+3+4+........+n) = 5^90

5^n(n+1) = 5^90

Comparing exponents, as base are equal,

n(n+1) =90

n^2+n-90= 0

n^2 + 10n-9n -90= 0

n(n+10) -9(n+10) =0

(n+10) (n-9) =0

either n+10=0, n=-10

Or, n-9=0, n=9