CPhill

Let's look at this again, rosala........

(2 / 3)  x 3  =

(2 /3) x (3 / 1)

6 / 3   =

2

4 + 4/4  + 4/4  =   

4 + 1 + 1  =

6

{There are surely other answers......!!!!   }     {  4! / 4  is another possibility, for instance }

log5x+log(x-1)= 2         Note.......   2 = log 100

log (5x * (x -1) )  =  log 100        and we can now just  ignore the logs and solve directly

5x ( x - 1)   = 100    simplify

5x^2 - 5x   = 100   

5x^2  - 5x  - 100  = 0      divide through by 5

x^2 - x - 20   = 0       factor

(x - 5) ( x + 4)  = 0        and setting both factors to 0 we have that  x = 5 or x  = -4

We must reject -4   because it makes the original logs negative......and that's undefined.....thus......

x = 5  is the solution

r = √[ (-12)² + (-15)² ]     =  √289   = 17

sin Θ = -15 / 17            csc Θ is the reciprocal

cos Θ = -12 / 17            sec Θ  is the reciprocal

tan Θ  = -15 / -12  =   15 / 12      cot Θ  is the reciprocal

8 + 9/84 =

8 + 3/28    =  227/3

3|2x-5|>21     divide both sides by 3

l 2x - 5 l > 7    and we can write

-7 > 2x - 5 > 7      add 5 to both sides

-2  > 2x > 12         divide both sides by 2

-1 > x > 6

So.....the solution set  is  ( -∞, -1) U  (6, ∞ )

20.3 mm

We'd need more info in order to solve this.........

If you're taking the floor of the term in the parentheses only, the answer is  1,604,128,023

If you're taking thr floor of the whole thing, the answer is 1,604,180,966