Pre-calc/trig question HELP PLEASE!?

Question

Please don't use a TI-83 calc, unless u do the answer right! We need to work it by hand??? Please help!!!

1) log 16 raised to the (1/4)=?

2) log 10 raised to the (0.01)=?

3) log 2 raised to the (1/8)=?

Answer 1

OK, there's 2 possibilities:
If you meant:
log (16^1/4), then you need to know the property of logarithms where:
log a^b = b log a.

So:
log 16^(1/4) = 1/4 log 16
log 10^(.01) = .01 log 10
log 2^(1/8) = 1/8 log 2

If you meant (log 16)^1/4, then I have no idea how to do it by hand.

Edit:
Further, you can also do things like:
log 16 = log 2^4 = 4 log 2
so 1/4 log 16 = 1/4 * 4 log 2 = log 2.

Answer 2

i dont have a scientific calculator with me right now so i can't tell you the answer but i can tell you how to solve it! first raise 16 to the 1/4 power, there should be an exponent button on your calculator, once you find the answer clear your calculator then press the log button followed by the answer you got for 16 to the 1/4. then you should get the answer! the same goes for the other problems, good luck, pre-cal is a pain!

Answer 3

cos(x/2) = sqrt(3) / 2 searching at a 30-60-ninety triangle, the cosine of 30 degrees, or pi/6 suits the bill, yet be careful to contain the equivalent attitude contained in the fourth quadrant for cosine x/2 = pi/6 OR x/2 = -pi/6 = 11pi/6 x = pi/3 or 11pi/3