Question

3^x X 9^4 = 3^n
Find n in terms of x

Answer 1

n = x + 8

Explanation:

Using the rules of exponents

`a^(m)` ×
`a^(n)` =
`a^((m+n))`

`(a^m)^(n)` =
`a^(mn)`

Then

`3^(x)` ×
`9^(4)` =
`3^(n)`

`3^(x)` ×
`(3^2)^(4)` =
`3^(n)`

`3^(x)` ×
`3^(8)` =
`3^(n)`

`3^(x+8)` =
`3^(n)`

Since bases on both sides are equal, both 3, then equate exponents

n = x + 8