Question

If 3^x-1 + 3^x+1 = 90, then x is equal to
(a) 0
(b) 1
(c) 2
(d) 3​

Answer 1

Answer:

(d) 3

Step-by-step explanation:

Take 3^x common from both 3^(x-1) and 3^(x+1) as the first step. After that solve the equation.

Here I shall use a basic concept of Index ::--

if a^x = a^m [ a≠1 ] then x=m [ where x is a variable and m is a real number ]

If a=1 , then x may or may not equal to m .

NOW,

3^(x-1) + 3^(x+1) = 90 , [ taking 3^x common ]

=> (⅓ + 3) • 3^x = 90 ,

=> 10/3 • 3^x = 90 ,

=> 3^x = 90 • 3/10 = 270/10 = 27 ,

=> 3^x = 3³

=> x=3 [ from the basic concept of index mentioned above ]

So the value of x is 3 .