ANSWER
[tex]b = - 1[/tex]
EXPLANATION
We want to find the value of b in the following exponential equation.
[tex] {5}^{3b - 1} = {5}^{b - 3} [/tex]
Since the base on both sides of the equation are the same.
We equate the exponents to get,
[tex]3b - 1 = b - 3[/tex]
We group like terms to obtain,
[tex]3b - b = - 3 + 1[/tex]
This will simplify to,
[tex]2b= - 2[/tex]
We now divide both sides by 2 to obtain,
[tex]b = - 1[/tex]
