ANSWER
[tex]y= log_{x}(p)[/tex]
EXPLANATION
The given expression is
[tex] {x}^{y} = p[/tex]
We take logarithm of both sides to base x.
[tex] log_{x}( {x}^{y} ) = log_{x}(p) [/tex]
Apply the power rule of logarithms to get:
[tex]ylog_{x}( {x}) = log_{x}(p)[/tex]
Logarithm of the base is 1.
This implies that,
[tex]y( 1) = log_{x}(p)[/tex]
[tex]y= log_{x}(p)[/tex]
