Question 810572
{{{(1/2)log(y,(p^3q^4))-(2/3)log(y,(p^4q^3))}}}
The coefficients of the logs are exponents of the logs.
{{{log(y,(p^3q^4)^(1/2))-log(y,(p^4q^3)^(2/3))}}}
You can combine the logs because they have the same base.
Since you are subtracting you will use the division property.
{{{log(y,((p^3q^4)^(1/2))/((p^4q^3)^(2/3)))}}}
simplify
{{{log(y,((p^(3/2)q^2)/(p^(8/3)q^2)))}}}
{{{log(y,((1)/(p^(7/6))))}}}
{{{log(y,((1)/(root(6,p^7))))}}}
{{{log(y,((1)/(p*root(6,p))))}}}
Rationalize
{{{log(y,((root(6,p))/(p^2)))}}}
There is the final answer.