Question

If 3^x—3^×–1= 6, then x^x is equal to​

Answer 1

Answer:

$x^{x}$ = 4

Step-by-step explanation:

6 can be written as 9 - 3 where 9 and 3 both are some powers of 3.

=> $3^{x} - 3^{x - 1}$ = 6

=> $3^{x} - 3^{x - 1}$ = 9 - 3

=> $3^{x} - 3^{x - 1}$ = 3² - $3^{1}$

Comparing, $3^{x}$ = 2 and $3^{x - 1}$ = $3^{1$

So, x = 2 and x - 1 = 1.

We can verify it by x - 1 = 1.

=> x = 2

Thus, $x^{x}$ = 2² => 4.