Answer:
The simplified expression is equal to log(9).
Explanation:
To condense the expression into a single logarithm, we can use the logarithmic identity that states that:
log(a*b) = log(a) + log(b)
First, we can simplify the expression inside the first set of parentheses:
2(log 18 - log 3) + 1/2 log 1/16
= 2log(18/3) + 1/2 log 1/16
= 2log(6) + 1/2 log 1/16
Next, we can simplify the expression inside the second set of parentheses using the logarithmic identity:
= 2log(6) + 1/2 log(1/16)
= 2log(6) + 1/2 log(1) - 1/2 log(16)
= 2*log(6) - 1/2 log(16)
Finally, we can use the logarithmic identity to condense the expression into a single logarithm:
= 2*log(6) - 1/2 log(16)
= log(6^2) - log(16^(1/2))
= log(36) - log(4)
= log(9)