To simplify this expression, we can use the properties of logarithms:

Logarithmic Property: log_b$xy$ = log_b$x$ + log_b$y$ Logarithmic Property: log_b$x^a$ = a * log_b$x$

Applying these properties,

log2 3 + log2 24 - 4 log4 3
= log2 $3<em>24$ - log4 3^4
= log2 72 - log4 81
= log2 $2^3</em>3^2$ - log4 $3^4$ = log2 2^3 + log2 3^2 - 4 log2 3
= 3 log2 2 + 2 log2 3 - 4 log2 3
= 3 + 2 * log2 3 - 4 log2 3
= 3 - 2 log2 3

Therefore, log2 3 + log2 24 - 4 log4 3 simplifies to 3 - 2 log2 3.