Question

Solve the following equation:

`3^(5x - 1) = root(4)(3)`

Answer 1

Given: `3^(5x - 1) = root(4)(3)`

Step-wise calculation:

1. Express the fourth root of 3 as an exponent:

`root(4)(3) = 3^(1/4)`

2. Set the exponents equal since the bases are the same (3):

`5x - 1 = 1/4`

3. Solve for (x):

`5x = 1 + 1/4`

`5x = 4/4 + 1/4`

`5x = 5/4`

`x = 5/4 ÷ 5`

`x = 5/4 xx 1/5`

`x = 1/4`