设x=log4 3(log以4为底3的对数）,求2的x次方+2的负x次方的值

题目

设x=log4 3(log以4为底3的对数）,求2的x次方+2的负x次方的值

答案

2∧x+2 ∧-x
=2∧log4 3+2∧-log4 3
=2∧1/2log2 3+2 ∧-1/2log2 3
=（2∧log2 3）∧1/2+（2∧log2 3）∧-1/2
=3∧1/2+3∧-1/2
=√￣3+√￣(1/3)
=√￣3+(√￣3)/3
=(4√￣3)/3