Please help me with this Math!! I dont understand it!! LOGS?

Question

I did so horribly on the test and now I need to do the test corrections for practice & extra credit. Please do some of these step by step so I can learn how to do them. Thanks!!!

5) if log 5=a, then log 250 can be expressed as...(its not one...i picked that and got it wrong
1) 50a 2) 2a+1 3)10+ 2a 4) 25a

6) solve for X. (1/2)^x =8 (huh?)

8) (x+3)^3 - (x-1)^0 (now i know anything to the 0 is 1)

15) If x is a positive integer, 8(x^2/3) is equivalent to....(use radical form)

Answer 1

250 = 5x5x10
log 5 = a; log 25 = 2a, log10=1
log 250 = log 25 + log 10 = 2a +1

(1/2)^x = 2 ^ -x = 2^3
-x = 3 x = -3

(x+3)^3 = x^3 + 9x^2 + 27x + 27 -1

x^2/3 = 3 rad(x^2)

Answer 2

Well, sorry to say that, but certainly one of your problem is that of reading/writing properly... For your problem #5, if log 5 = a, then log 250 is 3a + log 2, which is not among your answers so you must have made a mistake typing this.

For your problem #6, you take the log on both sides of the equation, remembering that log(a^b) = b log(a):
log((1/2)^x) = x log(1/2) = log(8), so
x = log(8)/log(1/2).

For your problem #8, what is the question?

For your problem #15, x^2/3 = (x^2)^1/3 = cubic root of x^2 etc. Good luck.

--Darth Maria