Question

若实数x满足等式log2x+2sina=3,则x-2的绝对值+(x-32)的绝对值的值是?

Answer 1

log2x+2sina=3

log2x=3-2sina

x=2^(3-2sina)

-1≤sina≤1

-2≤-2sina≤2

1≤3-2sina≤5

2^1≤2^(3-2sina)≤2^5

2≤x≤32

x-2的绝对值+(x-32)的绝对值

=x-2+32-x

=30