Question

Solve the following equation:

`5^(3x - 1) = root(3)(5)`

Answer 1

Given: `5^(3x - 1) = root(3)(5)`

Step-wise calculation:

1. Express the right-hand side with the same base as the left-hand side.

Since `root(3)(5)` can be written as `5^(1/3)`, we have:

`5^(3x - 1) = 5^(1/3)`

2. Since the bases are the same (both base 5), equate the exponents:

`3x - 1 = 1/3`

3. Solve for (x):

`3x = 1/3 + 1`

`3x = 1/3 + 3/3`

`3x = 4/3`

`x = 4/3 xx 1/3`

`x = 4/9`