Question

Solve the following equations.
√3 ⋅ 3^3x = 9

Answer 1

The solution is
`x = 0.5`

Explanation:

We need to write everything as a power of 3.

We know that:

`√(a) = a^(0.5)`

So

`√(3) = 3^(0.5)`

And

`9 = 3^(2)`

This following property is also important:

`(a^(b))/(a^(c)) = a^(b-c)`

To solve, the first step is putting everything with the variable x on one side and everything without the variable x on the other side

`√(3).3^(3x) = 9`

`3^(0.5).3^(3x) = 3^(2)`

`3^(3x) = (3^(2))/(3^(0.5))`

`3^(3x) = 3^(2-0.5)`

`3^(3x) = 3^(1.5)`

This means that:

`3x = 1.5`

`x = (1.5)/(3)`

`x = 0.5`