Verified answer

log(2^3)^5 + log 2^2

= log(2^15 * 2^2)

= log(2^17)

= 17log(2)

5 log 8 + log 4 =

5 log (2^3) + log (2^2) =

15 log 2 + 2 log 2 =

17 log 2

5 log 8 + log 4

= log 8^5 + log 4

= log (8^5 x 4)

= 5.Log(8) + Log(4)

= 5.Log(2³) + Log(2²)

= 15.Log(2) + 2.Log(2)

= 17.Log(2) ← it's good, but if you prefer:

= Log(2^17)