Answer:
Step-by-step explanation:
x = 180-65 = 115°
assuming you means k = log_2(3) [as log(2)3 is the same thing as 3log(2) due to multiplication being commutative]
given log(ab) = log(a) + log(b)
log_2(48) = log_2(3) + log_2(16)
X = 12
18/24 = .75
16 x .75 = 12
Q) Without a calculator, we must estimate the value of the following expression:
![3-\sqrt[]{38}.](https://tex.z-dn.net/?f=3-%5Csqrt%5B%5D%7B38%7D.)
A) I estimate 3 - √38 to be approximately -3.2.
First, we estimate the value of √38. √38 is between √36 and √49, but close to √36 (since 38 is closer to 4 than it is to 9). Since √36 is 6, √38 is probably something like 6.1 or 6.2. Filling 6.2 in the expression and simplifying, we have this:

So, I expect the number 3 - √38 to be close to -3.2.
Using a calculator we find that: 3 - √38 ≅ -3.16, which it is approximately the result that we found.
Answer
Without a calculator we find that 3 - √38 ≅ -3.2.