If 6^(n + 5) - 6^(n + 3) = 7560, What is the value of n?

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09 May 2017 Root and Power

If 6^(n + 5) - 6^(n + 3) = 7560, What is the value of n?

OPtion

1) 5
2) 3
3) 4
4) 1
5) -1
6) 2
7) -3
8) -2
9) -4
10) None of these

Solution

6^(n + 5) - 6^(n + 3) = 7560

=> 6^(n + 3 + 2) - 6^(n + 3) = 7560

=> 6^(n + 3) × 6^(2) - 6^(n + 3) = 7560

=> 6^(n + 3)[6^(2) - 1] = 7560

=> 6^(n + 3) × (35) = 7560

=> 6^(n + 3) = 216

=> 6^(n + 3) = 6^3

=> n + 3 = 3
=> n = 0

Correct Option: 10 Best Solution (14)

A.P.Singh   7 years AGO

[6^(n+3)][6^2-1]= 7560
6^(n+3)=216=6^3
n+3=3
n=0

Like? Yes (3) | No   

Haritha Mummidivarapu   7 years AGO

x^(a+b) = x^a * x^b,
6^n * 6^5 - 6^n * 6^3 = 6^n( 6^5 - 6^3)
= 6^n(7776 - 216)
= 6^n(7560) = 7560 (given)
so by equating, 6^n = 1 => n=0

Like? Yes (2) | No (2)  

G.S.Kantharao   7 years AGO

6^(n+5) -6^(n+3)=6^n(6^5-6^3)=7560
6^n(7776-216)=6^n(7560)=7560
6^n=7560/7560=1=6^0
Hence n=0
Then the right option is 10.

Like? Yes (2) | No (2)  

Mukund Manohar   7 years AGO

6^(n+5) - 6^(n+3) = 7560
=> (6^n * 6^5) - (6^n * 6^3) = 7560
=> 6^n(6^5 - 6^3) = 7560
=> 6^n * 7560 = 7560
=> 6^n = 1
=> 6^n = 6^0
Value of n = 0

Like? Yes (2) | No (2)  

Vahira Bollina   7 years AGO

6^(n+5) - 6^(n+3) = 7560
formulae :a^(m+n)=a^m*a^n
the above equation can be written as
(6^n * 6^5)-(6^n * 6^3)=7560
6^n(6^5 - 6^3)=7560
6^n(7560)=7560
6^n=1
1 can be written as 6^0
6^n=6^0
n=0

Like? Yes (1) | No (1)  

vimal tiwari   7 years AGO

6^(n+3)(6^2 - 1) = 7560

6^(n+3) = 7560/35
6^(n+3)=6^3

n+3=3
n=0

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ganesh chemanchula   7 years AGO

6^n*6^5-6^n*6^3=7560
6^n(6^5-6^3)=7560
6^n*7560=7560
6^n=1
6^n=6^0
by comparing n=0

Like? Yes | No   

Avinash Bamboria   7 years AGO

answer must be 0, 6^n*6^5-6^n*6^3=7560,
6^n(6^5-6^3)=7560
6^n=1
n=0

Like? Yes | No   

jyothi chhabria   7 years AGO

6^n(6^5-6^3)=7560
6^n×7560=7560
6^n=1
if n=0 then it's 1 so
n=0

Like? Yes | No (1)  

Siva   7 years AGO

n must be 0,
6^(n+5)-6^(n+3)=7560
(6^n)(6^5-6^3)=7560
6^n=1 => n=0.

Like? Yes | No (1)  

Bupathikavya   7 years AGO

Given 6^n * 6^5 - 6^n * 6^3 = 7560
6^n(6^5 - 6^3) = 7560
6^n(7560) = 7560
6^n = 1
6^0 = 1
n = 0

Like? Yes | No (1)  

Devesh Gupta   7 years AGO

6^(n+5)-6^(n+3)=7560
6^n * 6^3 (36-1)=7560
6^n = 7560/(35*216)=1
6^n=6^0=1

n=0 Ans

Like? Yes | No (1)  

Amarnath Kumar Upadhyay   7 years AGO

6^(n+5)-6^(n+3)=7560
6^n * 6^5 - 6^n * 6^3=7560
6^n *6^3(6^2-1)=7560
6^n=1
6^n=6^0
n=0 ans

Like? Yes | No (1)  

Neha Nema   7 years AGO

n=0
6^(n+5)-6^(n+3)=7560
7560=6^3*35
6^n*6^3(6^2-1)= 6^n*6^3*(35)=rhs
=> 6^n*6^3*35 = 6^3*35
=> 6^n= 1
n=0

Like? Yes | No (1)