log(√6) = log(6^1/2)
We can factor out 6^1/2 using 2 and 3.
log(6^1/2) = log(2^1/2 * 3^1/2)
Rewrite it using the power rule [ [tex]\text{log}_ax^p=p~\text{log}_ax[/tex] ] and product rule [ [tex]\text{log}_a(xy)=log_ax+log_ay[/tex] ]
log(2^1/2 * 3^1/2) = 1/2 log(2) + 1/2 log(3)
Simplify using the given values.
1/2(0.3010) + 1/2(0.4771)
0.1505 + 0.23855
0.38905
Therefore, log(√6) = 0.38905
Best of Luck!
