Question

How do i solve for x? thank you!

Answer 1

x = 3.5

Step-by-step explanation

Using the rules of exponents

`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))` and
`√(a)` =
`a^{(1)/(2) }`

Then

36
`√(6)` = 6² ×
`6^{(1)/(2) }` =
`6^((2+0.5))` =
`6^(2.5)`

Thus

`6^(x-1)` =
`6^(2.5)`

Since the bases on both sides are equal, both 6, equate the exponents

x - 1 = 2.5 ( add 1 to both sides )

x = 3.5

Answer 2

`x = (7)/(2)`

Explanation:

`6^(x-1) = 36 \sqrt6\\\\6^(x-1) = 6^2 * 6^{(1)/(2)}\\\\6^(x-1) = 6^{2 + (1)/(2) }`
`[ \ a^x * a^ y = a^(x+ y) \ ]`

`x - 1 = 2 + (1)/(2)`
`[ \ b^x = b^y => x = y \ ]`

`x = 2 + (1)/(2) + 1\\\\x = 3 + (1)/(2) \\\\x = (6+ 1)/(2) \\\\x = (7)/(2)`