# How do you simplify 4^(log_2 [log_ 2(x^2+24x))]?

Jun 17, 2016

I tried writing $4$ as $2 \cdot 2$:
${\left(2 \cdot 2\right)}^{{\log}_{2} \left[{\log}_{2} \left({x}^{2} + 24 x\right)\right]} = {2}^{{\log}_{2} \left[{\log}_{2} \left({x}^{2} + 24 x\right)\right]} \cdot {2}^{{\log}_{2} \left[{\log}_{2} \left({x}^{2} + 24 x\right)\right]} =$
$= {\cancel{2}}^{\cancel{{\log}_{2}} \left[{\log}_{2} \left({x}^{2} + 24 x\right)\right]} \cdot {\cancel{2}}^{\cancel{{\log}_{2}} \left[{\log}_{2} \left({x}^{2} + 24 x\right)\right]} =$
$= {\log}_{2} \left({x}^{2} + 24 x\right) {\log}_{2} \left({x}^{2} + 24 x\right)$