Question

log4×log2×log3(x)≤5​

Answer 1

$log_4log_2log_3x\leq 5\; \; ,\; \; \; ODZ:\; x>0\\\\log_4(log_2log_3x)\leq log_44^5\; \; \; \Rightarrow \; \; \; log_2log_3x\leq 4^5\; ,\; \; log_2log_3x\leq 1024\; ,\\\\log_2(log_3x)\leq log_22^{1024}\; \; \; \Rightarrow \; \; \; log_3x\leq 2^{1024}\; ,\\\\log_3x\leq log_33^{2^{1024}}\; \; \; \Rightarrow \; \; \; x\leq 3^{2^{1024}}\\\\Otvet:\; \; 0<x\leq 3^{2^{1024}}\; \; \; ili\; \; \; \; 0<x\leq 3^{2^{2^{10}}}\; .$