Given That Log 8 5 = 0 $\log _ { 8 } \sqrt [ 7 ] { 11 }$

Short Answer

Given that log 8 5 = 0.7740 and log 8 11 = 1.1531, evaluate the expression $\log _ { 8 } \sqrt [ 7 ] { 11 }$ by using properties: For positive real numbers b , r and s , where b $\neq$ 1, and for any real number p , $\log b r s = \log _ { b } r + \log _ { b } s$ $\log b \frac { r } { s } = \log{ b }^ r - \log b^ s$ $\log _ { b } r ^ { p } = p \left( \log _ { b } r \right)$ Please give the answer to four decimal places.