Question

if 3^n =729, and (3^(n-1))(x^(n-2))=3(18^4), what is the value of n+x

Answer 1

√3^n=729 ,

729= 27^2 ,

√3^n=27^2

3^n=(27^2)^2

3^n=27^4 *// (a^m)^n = a^m×n //* #1

3^n= (3^3)^4 //* 3 is the cube root of 27//*#2

3^n=3^12 //* as #1 rule

So n =12

Answer 2

Answer:

the value of n+x is 12

Step-by-step explanation:

i)

=> 3^n = 729

=> 3^6 = 729

=> n = 6

ii) substitute the 'n' value

=> (3^n-1) (x^n-2) = 3(18^4)

=> (3^5) (x^4) = 3(3^4 * 6^4)

=> x=6

iii) Answer:

=> n + x = 6 + 6 = 12