# Find n is the equation 52 × 54 × 56 × … × 52n = (0.008)-30.

am× an = am + n

LHS = 52 × 54 × 56 × … × 52n

= 52 + 4 + 6 + …2n

= 52(1 + 2 + 3 + …n)

{1 + 2 + 3 + …n = }

=

= 5n(n + 1)

RHS = (0.008)-30 = (8× 10-3)-30

= (23× (2×5)-3)-30

= (23× 2-3× 5-3)-30

= 590

(am)n = amn

LHS = RHS

5n(n + 1) = 590

n(n + 1) = 90

n2 + n-90 = 0

Solving for n,

n = 9 and n = -10

But, n<0 is not possible

Hence, n = 9

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Arithmetic Progression34 mins
Champ Quiz | Arithmetic Progression30 mins
Quiz | Arithmetic Progression44 mins
Smart Revision | Arithmetic Progression47 mins
Smart Revision | General Term of an A.P44 mins
NCERT | Fundamental Theorem Of Arithmetic45 mins
Lets Check Your Knowledge in A.P.49 mins
Quiz on Arithmetic Progression Quiz32 mins
NCERT | Arithmetic Progression36 mins
Fundamental Theorem of Arithmetic- 143 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses