Question 203466
{{{log(2, (a^2*sqrt(b))^4)}}}
{{{log(2, (a^8)) + log(2, (sqrt(b)^4))}}}
Is good so far. We can simplify the 2nd log by using the fact that a square root is the same as an exponent of 1/2:
{{{log(2, (a^8)) + log(2, ((b^(1/2))^4))}}}
{{{log(2, (a^8)) + log(2, (b^2))}}}
This is a sum of logarithms. I'm not sure what "Express as powers of factors" means. But I am guessing that the next simplification is desired. We can use the following property of logarithms: {{{log((x^y)) = y*log(x)}}}. This allows us to "move" an exponent from the argument "out in front":
{{{8log(2, (a)) + 2log(2, (b))}}}