Find the exact value of the logarithmic expression without u

Find the exact value of the logarithmic expression without using a calculator. (If not possible, enter IMPOSSIBLE.) log_2 5 squareroot 16

Solution

log₂ ⁵16

^ma=a^1/m

=log₂ (16)^1/5

=log₂ (2⁴)^1/5

(a^m)ⁿ =a^mn

=log₂ 2^4/5

log_b a^m= m log_ba

=(4/5)*log₂ 2

=(4/5)*1

=4/5