`|{:(5sqrt(log_(e)3),,5sqrt(log_(e)3),,3sqrt(log_(e)3)),(3^(-log_(1//3)4),,(0.1)^(log_(0.01)4),,7^(log_(7)3)),(7,,3,,5):}|" is equal to ""____"`

Answer

0

Explanation

`Delta = |{:(5sqrt(log_(5)3),,5sqrt(log_(5)3),,3sqrt(log_(3)5)),(3^(-log_(1//3)4),,(0.1)^(log_(0.01)4),,7^(log_(7)3)),(7,,3,,5):}|`
`= |{:(5sqrt(log_(5)3),,5sqrt(log_(5)3),,3sqrt(log_(3)5)),(3^(log_(1//3)4),,(0.1)^(log_(0.01)2),,7^(log_(7)3)),(7,,3,,5):}|`
` = |{:(5sqrt(log_(5)3),,5sqrt(log_(5)3),,3sqrt(log_(3)5)),(4,,2,,3),(7,,3,,5):}|`
Applying `C_(2) to C_(2) -C_(1) " and " C_(3) to C_(3)-C_(1)` we get
`Delta = |{:(5sqrt(log_(5)3),,0,,0),(4,,-2,,-1),(7,,-4,,-2):}|=0`